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186350686 | 10.1007/s00018-015-2038-4 | Systemic inflammation and infections are associated with neurodegenerative diseases. Unfortunately, the molecular bases of this link are still largely undiscovered. We, therefore, review how inflammatory processes can imbalance membrane homeostasis and theorize how this may have an effect on the aggregation behavior of the proteins implicated in such diseases. Specifically, we describe the processes that generate such imbalances at the molecular level, and try to understand how they affect protein folding and localization. Overall, current knowledge suggests that microglia pro-inflammatory mediators can generate membrane damage, which may have an impact in terms of triggering or accelerating disease manifestation | Is membrane homeostasis the missing link between inflammation and neurodegenerative diseases? | is membrane homeostasis the missing link between inflammation and neurodegenerative diseases? | systemic inflammation infections neurodegenerative diseases. unfortunately bases largely undiscovered. inflammatory imbalance homeostasis theorize aggregation implicated diseases. imbalances folding localization. microglia inflammatory mediators triggering accelerating manifestation | non_dup | [] |
77145364 | 10.1007/s00018-015-2059-z | The paracaspase MALT1 has a central role in the activation of lymphocytes and other immune cells including myeloid cells, mast cells and NK cells. MALT1 activity is required not only for the immune response, but also for the development of natural Treg cells that keep the immune response in check. Exaggerated MALT1 activity has been associated with the development of lymphoid malignancies, and recently developed MALT1 inhibitors show promising anti-tumor effects in xenograft models of diffuse large B cell lymphoma. In this review, we provide an overview of the present understanding of MALT1's function, and discuss possibilities for its therapeutic targeting based on recently developed inhibitors and animal models | The paracaspase MALT1: biological function and potential for therapeutic inhibition. | the paracaspase malt1: biological function and potential for therapeutic inhibition. | paracaspase malt lymphocytes immune myeloid mast cells. malt immune treg keep immune check. exaggerated malt lymphoid malignancies malt inhibitors promising xenograft diffuse lymphoma. overview malt possibilities therapeutic targeting inhibitors | non_dup | [] |
33638164 | 10.1007/s00018-015-2075-z | The cellular defense system known as global-genome nucleotide excision repair (GG-NER) safeguards genome stability by eliminating a plethora of structurally unrelated DNA adducts inflicted by chemical carcinogens, ultraviolet (UV) radiation or endogenous metabolic by-products. Xeroderma pigmentosum group C (XPC) protein provides the promiscuous damage sensor that initiates this versatile NER reaction through the sequential recruitment of DNA helicases and endonucleases, which in turn recognize and excise insulting base adducts. As a DNA damage sensor, XPC protein is very unique in that it (a) displays an extremely wide substrate range, (b) localizes DNA lesions by an entirely indirect readout strategy, (c) recruits not only NER factors but also multiple repair players, (d) interacts avidly with undamaged DNA, (e) also interrogates nucleosome-wrapped DNA irrespective of chromatin compaction and (f) additionally functions beyond repair as a co-activator of RNA polymerase II-mediated transcription. Many recent reports highlighted the complexity of a post-translational circuit that uses polypeptide modifiers to regulate the spatiotemporal activity of this multiuse sensor during the UV damage response in human skin. A newly emerging concept is that stringent regulation of the diverse XPC functions is needed to prioritize DNA repair while avoiding the futile processing of undamaged genes or silent genomic sequences | Xeroderma pigmentosum group C sensor: unprecedented recognition strategy and tight spatiotemporal regulation | xeroderma pigmentosum group c sensor: unprecedented recognition strategy and tight spatiotemporal regulation | defense nucleotide excision repair safeguards eliminating plethora structurally unrelated adducts inflicted carcinogens ultraviolet endogenous metabolic products. xeroderma pigmentosum promiscuous sensor initiates versatile sequential recruitment helicases endonucleases recognize excise insulting adducts. sensor displays extremely localizes lesions entirely indirect readout recruits repair players interacts avidly undamaged interrogates nucleosome wrapped irrespective chromatin compaction additionally repair activator polymerase transcription. highlighted translational circuit polypeptide modifiers regulate spatiotemporal multiuse sensor skin. newly emerging stringent diverse prioritize repair avoiding futile undamaged silent genomic | non_dup | [] |
53358165 | 10.1007/s00018-015-2084-y | Spinal muscular atrophy (SMA) is a devastating motoneuron (MN) disorder caused by homozygous loss of SMN1. Rarely, SMN1-deleted individuals are fully asymptomatic despite carrying identical SMN2 copies as their SMA III-affected siblings suggesting protection by genetic modifiers other than SMN2. High plastin 3 (PLS3) expression has previously been found in lymphoblastoid cells but not in fibroblasts of asymptomatic compared to symptomatic siblings. To find out whether PLS3 is also upregulated in MNs of asymptomatic individuals and thus a convincing SMA protective modifier, we generated induced pluripotent stem cells (iPSCs) from fibroblasts of three asymptomatic and three SMA III-affected siblings from two families and compared these to iPSCs from a SMA I patient and control individuals. MNs were differentiated from iPSC-derived small molecule neural precursor cells (smNPCs). All four genotype classes showed similar capacity to differentiate into MNs at day 8. However, SMA I-derived MN survival was significantly decreased while SMA III- and asymptomatic-derived MN survival was moderately reduced compared to controls at day 27. SMN expression levels and concomitant gem\ud
numbers broadly matched SMN2 copy number distribution; SMA I presented the lowest levels, whereas SMA III and asymptomatic showed similar levels. In contrast, PLS3 was significantly upregulated in mixed MN cultures from asymptomatic individuals pinpointing a tissue-specific regulation. Evidence for strong PLS3 accumulation in shaft and rim of growth cones in MN cultures from asymptomatic individuals implies an important role in neuromuscular synapse formation and maintenance. These findings provide strong evidence that PLS3 is a genuine SMA protective modifier | Plastin 3 is upregulated in iPSC-derived motoneurons from asymptomatic SMN1-deleted individuals | plastin 3 is upregulated in ipsc-derived motoneurons from asymptomatic smn1-deleted individuals | spinal muscular atrophy devastating motoneuron disorder homozygous rarely deleted asymptomatic carrying copies siblings protection modifiers plastin lymphoblastoid fibroblasts asymptomatic symptomatic siblings. upregulated asymptomatic convincing protective modifier pluripotent ipscs fibroblasts asymptomatic siblings families ipscs individuals. differentiated ipsc molecule precursor smnpcs genotype differentiate asymptomatic moderately concomitant broadly matched copy asymptomatic levels. upregulated cultures asymptomatic pinpointing regulation. accumulation shaft cones cultures asymptomatic neuromuscular synapse maintenance. genuine protective modifier | non_dup | [] |
153520983 | 10.1007/s00018-015-2101-1 | Parkinson's disease (PD is a progressive neurological disorder characterized by the degeneration and death of midbrain dopamine and non-dopamine neurons in the brain leading to motor dysfunctions and other symptoms, which seriously influence the quality of life of PD patients. The drug L-dopa can alleviate the motor symptoms in PD, but so far there are no rational therapies targeting the underlying neurodegenerative processes. Despite intensive research, the molecular mechanisms causing neuronal loss are not fully understood which has hampered the development of new drugs and disease-modifying therapies. Neurotrophic factors are by virtue of their survival promoting activities attract candidates to counteract and possibly halt cell degeneration in PD. In particular, studies employing glial cell line-derived neurotrophic factor (GDNF) and its family member neurturin (NRTN), as well as the recently described cerebral dopamine neurotrophic factor (CDNF) and the mesencephalic astrocyte-derived neurotrophic factor (MANF) have shown positive results in protecting and repairing dopaminergic neurons in various models of PD. Other substances with trophic actions in dopaminergic neurons include neuropeptides and small compounds that target different pathways impaired in PD, such as increased cell stress, protein handling defects, dysfunctional mitochondria and neuroinflammation. In this review, we will highlight the recent developments in this field with a focus on trophic factors and substances having the potential to beneficially influence the viability and functions of dopaminergic neurons as shown in preclinical or in animal models of PD | Current disease modifying approaches to treat Parkinson's disease | current disease modifying approaches to treat parkinson's disease | parkinson progressive neurological disorder degeneration midbrain dopamine dopamine motor dysfunctions seriously patients. dopa alleviate motor rational therapies targeting neurodegenerative processes. intensive causing neuronal understood hampered drugs modifying therapies. neurotrophic virtue promoting attract candidates counteract possibly halt degeneration employing glial neurotrophic gdnf member neurturin nrtn cerebral dopamine neurotrophic cdnf mesencephalic astrocyte neurotrophic manf protecting repairing dopaminergic substances trophic dopaminergic neuropeptides pathways impaired handling defects dysfunctional mitochondria neuroinflammation. highlight developments trophic substances beneficially viability dopaminergic preclinical | non_dup | [] |
82970597 | 10.1007/s00018-015-2117-6 | A fusion between the EML4 (echinoderm microtubule-associated protein-like) and ALK (anaplastic lymphoma kinase) genes was identified in non-small cell lung cancer (NSCLC) in 2007 and there has been rapid progress in applying this knowledge to the benefit of patients. However, we have a poor understanding of EML4 and ALK biology and there are many challenges to devising the optimal strategy for treating EML4-ALK NSCLC patients. In this review, we describe the biology of EML4 and ALK, explain the main features of EML4-ALK fusion proteins and outline the therapies that target EML4-ALK. In particular, we highlight the recent advances in our understanding of the structures of EML proteins, describe the molecular mechanisms of resistance to ALK inhibitors and assess current thinking about combinations of ALK drugs with inhibitors that target other kinases or Hsp90.Peer-reviewedPublisher Versio | Molecular mechanisms that underpin EML4-ALK driven cancers and their response to targeted drugs | molecular mechanisms that underpin eml4-alk driven cancers and their response to targeted drugs | fusion echinoderm microtubule anaplastic lymphoma nsclc progress benefit patients. challenges devising treating nsclc patients. fusion outline therapies alk. highlight advances inhibitors thinking combinations drugs inhibitors kinases .peer reviewedpublisher versio | non_dup | [] |
42942959 | 10.1007/s00018-015-2118-5 | The ATP-binding cassette (ABC) transporters of class G display a different domain organisation than P-glycoprotein/ABCB1 and bacterial homologues with a nucleotide-binding domain preceding the transmembrane domain. The linker region connecting these domains is unique and its function and structure cannot be predicted. Sequence analysis revealed that the human ABCG2 linker contains a LSGGE sequence, homologous to the canonical C-motif/ABC signature present in all ABC nucleotide-binding domains. Predictions of disorder and of secondary structures indicated that this C2-sequence was highly mobile and located between an alpha-helix and a loop similarly to the C-motif. Point mutations of the two first residues of the C2-sequence fully abolished the transport-coupled ATPase activity, and led to the complete loss of cell resistance to mitoxantrone. The interaction with potent, selective and non-competitive, ABCG2 inhibitors was also significantly altered upon mutation. These results suggest an important mechanistic role for the C2-sequence of the ABCG2 linker region in ATP binding and/or hydrolysis coupled to drug efflux | The linker region of breast cancer resistance protein ABCG2 is critical for coupling of ATP-dependent drug transport. | the linker region of breast cancer resistance protein abcg2 is critical for coupling of atp-dependent drug transport. | cassette transporters display organisation glycoprotein abcb bacterial homologues nucleotide preceding transmembrane domain. linker connecting predicted. abcg linker lsgge homologous canonical motif signature nucleotide domains. disorder mobile alpha helix motif. abolished atpase mitoxantrone. potent selective competitive abcg inhibitors altered mutation. mechanistic abcg linker hydrolysis efflux | non_dup | [] |
84348494 | 10.1007/s00018-015-2119-4 | Nicotinamide adenine dinucleotide (NAD+) is a vital molecule found in all living cells. NAD+ intracellular levels are dictated by its synthesis, using the de novo and/or salvage pathway, and through its catabolic use as co-enzyme or co-substrate. The regulation of NAD+ metabolism has proven to be an adequate drug target for several diseases, including cancer, neurodegenerative or inflammatory diseases. Increasing interest has been given to NAD+ metabolism during innate and adaptive immune responses suggesting that its modulation could also be relevant during host-pathogen interactions. While the maintenance of NAD+ homeostatic levels assures an adequate environment for host cell survival and proliferation, fluctuations in NAD+ or biosynthetic precursors bioavailability have been described during host-pathogen interactions, which will interfere with pathogen persistence or clearance. Here, we review the double-edged sword of NAD+ metabolism during host-pathogen interactions emphasizing its potential for treatment of infectious diseases.JG was supported by PD/BD/106053/2015. BV was supported by IRD (Institut de Recherche pour le Développement) institutional funding. JE was supported by a European Community’s Seventh Framework Program under grant agreement No. 602773 (Project KINDRED), an ANR grant (LEISH-APO, France) and a Partenariat Hubert Curien (PHC) (program Volubilis, MA/11/262). JE also thanks the Canada Research Chair program for his support. RS thank FCT—Foundation for Science and Technology—for their Investigator FCT Grant (IF/00021/2014)info:eu-repo/semantics/publishedVersio | Exploring NAD(+) metabolism in host-pathogen interactions | exploring nad(+) metabolism in host-pathogen interactions | nicotinamide adenine dinucleotide vital molecule living cells. intracellular dictated novo salvage catabolic enzyme substrate. metabolism proven adequate neurodegenerative inflammatory diseases. metabolism innate adaptive immune modulation pathogen interactions. maintenance homeostatic assures adequate proliferation biosynthetic precursors bioavailability pathogen interfere pathogen persistence clearance. edged sword metabolism pathogen emphasizing infectious diseases.jg institut recherche pour développement institutional funding. community’s seventh kindred leish partenariat hubert curien volubilis thanks canada chair support. fct—foundation technology—for investigator info repo semantics publishedversio | non_dup | [] |
143897771 | 10.1007/s00018-016-2138-9 | Most natural protein sequences have resulted from millions or even billions of years of evolution. How they differ from random sequences is not fully understood. Previous computational and experimental studies of random proteins generated from noncoding regions yielded inclusive results due to species-dependent codon biases and GC contents. Here, we approach this problem by investigating 10,000 sequences randomized at the amino acid level. Using well-established predictors for protein intrinsic disorder, we found that natural sequences have more long disordered regions than random sequences, even when random and natural sequences have the same overall composition of amino acid residues. We also showed that random sequences are as structured as natural sequences according to contents and length distributions of predicted secondary structure, although the structures from random sequences may be in a molten globular-like state, according to molecular dynamics simulations. The bias of natural sequences toward more intrinsic disorder suggests that natural sequences are created and evolved to avoid protein aggregation and increase functional diversity.Full Tex | Natural protein sequences are more intrinsically disordered than random sequences | natural protein sequences are more intrinsically disordered than random sequences | resulted millions billions evolution. understood. noncoding yielded inclusive codon biases contents. investigating randomized level. predictors intrinsic disorder disordered residues. structured contents molten globular simulations. toward intrinsic disorder created evolved avoid aggregation diversity.full | non_dup | [] |
55715249 | 10.1007/s00018-016-2189-y | Necroptosis was initially identified as a backup cell death program when apoptosis is blocked. However, it is now recognized as a cellular defense mechanism against infections and is presumed to be a detrimental factor in several pathologies driven by cell death. Necroptosis is a prototypic form of regulated necrosis that depends on activation of the necrosome, which is a protein complex in which receptor interacting protein kinase (RIPK) 3 is activated. The RIP homotypic interaction motif (RHIM) is the core domain that regulates activation of the necrosome. To date, three RHIM-containing proteins have been reported to activate the kinase activity of RIPK3 within the necrosome: RIPK1, Toll/IL-1 receptor domain-containing adaptor inducing IFN-beta (TRIF), and DNA-dependent activator of interferon regulatory factors (DAI). Here, we review and discuss commonalities and differences of the increasing number of activators of the necrosome. Since the discovery that activation of mixed lineage kinase domain-like (MLKL) by RIPK3 kinase activity is crucial in necroptosis, interest has increased in monitoring and therapeutically targeting their activation. The availability of new phospho-specific antibodies, pharmacologic inhibitors, and transgenic models will allow us to further document the role of necroptosis in degenerative, inflammatory and infectious diseases | An outline of necrosome triggers | an outline of necrosome triggers | necroptosis initially backup apoptosis blocked. recognized defense infections presumed detrimental pathologies death. necroptosis prototypic regulated necrosis necrosome interacting ripk activated. homotypic motif rhim regulates necrosome. rhim activate ripk necrosome ripk toll adaptor inducing beta trif activator interferon regulatory commonalities activators necrosome. discovery lineage mlkl ripk crucial necroptosis therapeutically targeting activation. availability phospho antibodies pharmacologic inhibitors transgenic document necroptosis degenerative inflammatory infectious | non_dup | [] |
84040508 | 10.1007/s00018-016-2191-4 | Tumor necrosis factor (TNF) is a master pro-inflammatory cytokine, and inappropriate TNF signaling is implicated in the pathology of many inflammatory diseases. Ligation of TNF to its receptor TNFR1 induces the transient formation of a primary membrane-bound signaling complex, known as complex I, that drives expression of pro-survival genes. Defective complex I activation results in induction of cell death, in the form of apoptosis or necroptosis. This switch occurs via internalization of complex I components and assembly and activation of secondary cytoplasmic death complexes, respectively known as complex II and necrosome. In this review, we discuss the crucial regulatory functions of ubiquitination-a post-translational protein modification consisting of the covalent attachment of ubiquitin, and multiples thereof, to target proteins-to the various steps of TNFR1 signaling leading to necroptosis | Poly-ubiquitination in TNFR1-mediated necroptosis | poly-ubiquitination in tnfr1-mediated necroptosis | necrosis master inflammatory cytokine inappropriate implicated pathology inflammatory diseases. ligation tnfr induces transient drives genes. defective apoptosis necroptosis. switch internalization assembly cytoplasmic complexes necrosome. crucial regulatory ubiquitination translational modification consisting covalent attachment ubiquitin multiples thereof tnfr necroptosis | non_dup | [] |
77413120 | 10.1007/s00018-016-2255-5 | The ability of ubiquitin to form up to eight different polyubiquitin chain linkages generates complexity within the ubiquitin proteasome system, and accounts for the diverse roles of ubiquitination within the cell. Understanding how each type of ubiquitin linkage is correctly interpreted by ubiquitin binding proteins provides important insights into the link between chain recognition and cellular fate. A major function of ubiquitination is to signal degradation of intracellular proteins by the 26S proteasome. Lysine-48 (K48) linked polyubiquitin chains are well established as the canonical signal for proteasomal degradation, but recent studies show a role for other ubiquitin linked chains in facilitating degradation by the 26S proteasome. Here, we review how different types of polyubiquitin linkage bind to ubiquitin receptors on the 26S proteasome, how they signal degradation and discuss the implications of ubiquitin chain linkage in regulating protein breakdown by the proteasome.JAN is supported by a Wellcome Trust Senior Clinical Research Fellowship (102770/Z/13/Z). The Cambridge Institute for Medical Research is in receipt of a Wellcome Trust Strategic Award (100140).This is the final published version. It first appeared from Springer via https://doi.org/10.1007/s00018-016-2255- | The recognition of ubiquitinated proteins by the proteasome | the recognition of ubiquitinated proteins by the proteasome | ubiquitin eight polyubiquitin linkages generates ubiquitin proteasome accounts diverse roles ubiquitination cell. ubiquitin linkage correctly interpreted ubiquitin insights recognition fate. ubiquitination degradation intracellular proteasome. lysine polyubiquitin chains canonical proteasomal degradation ubiquitin chains facilitating degradation proteasome. polyubiquitin linkage bind ubiquitin receptors proteasome degradation ubiquitin linkage regulating breakdown proteasome.jan wellcome trust senior fellowship receipt wellcome trust strategic award .this version. appeared springer | non_dup | [] |
143897958 | 10.1007/s00018-016-2267-1 | Antibodies to blood-stage antigens of Plasmodium falciparum play a pivotal role in human immunity to malaria. During parasite development, multiple proteins are trafficked from the intracellular parasite to the surface of P. falciparum-infected erythrocytes (IEs). However, the relative importance of different proteins as targets of acquired antibodies, and key pathways involved in trafficking major antigens remain to be clearly defined. We quantified antibodies to surface antigens among children, adults, and pregnant women from different malaria-exposed regions. We quantified the importance of antigens as antibody targets using genetically engineered P. falciparum with modified surface antigen expression. Genetic deletion of the trafficking protein skeleton-binding protein-1 (SBP1), which is involved in trafficking the surface antigen PfEMP1, led to a dramatic reduction in antibody recognition of IEs and the ability of human antibodies to promote opsonic phagocytosis of IEs, a key mechanism of parasite clearance. The great majority of antibody epitopes on the IE surface were SBP1-dependent. This was demonstrated using parasite isolates with different genetic or phenotypic backgrounds, and among antibodies from children, adults, and pregnant women in different populations. Comparisons of antibody reactivity to parasite isolates with SBP1 deletion or inhibited PfEMP1 expression suggest that PfEMP1 is the dominant target of acquired human antibodies, and that other P. falciparum IE surface proteins are minor targets. These results establish SBP1 as part of a critical pathway for the trafficking of major surface antigens targeted by human immunity, and have key implications for vaccine development, and quantifying immunity in populations.Full Tex | A single point in protein trafficking by Plasmodium falciparum determines the expression of major antigens on the surface of infected erythrocytes targeted by human antibodies | a single point in protein trafficking by plasmodium falciparum determines the expression of major antigens on the surface of infected erythrocytes targeted by human antibodies | antibodies antigens plasmodium falciparum pivotal immunity malaria. parasite trafficked intracellular parasite falciparum erythrocytes targets acquired antibodies pathways trafficking antigens defined. quantified antibodies antigens adults pregnant malaria exposed regions. quantified antigens targets genetically engineered falciparum antigen expression. deletion trafficking skeleton trafficking antigen pfemp dramatic recognition antibodies promote opsonic phagocytosis parasite clearance. great majority epitopes dependent. parasite isolates phenotypic backgrounds antibodies adults pregnant populations. comparisons reactivity parasite isolates deletion inhibited pfemp pfemp acquired antibodies falciparum minor targets. establish trafficking antigens targeted immunity vaccine quantifying immunity populations.full | non_dup | [] |
76945918 | 10.1007/s00018-016-2297-8 | YesThe extracellular signal-regulated kinase 1/2
(ERK1/2) mitogen-activated protein kinase (MAPK) signalling
pathway regulates many cellular functions,
including proliferation, differentiation, and transformation.
To reliably convert external stimuli into specific cellular
responses and to adapt to environmental circumstances, the
pathway must be integrated into the overall signalling
activity of the cell. Multiple mechanisms have evolved to
perform this role. In this review, we will focus on negative
feedback mechanisms and examine how they shape ERK1/
2 MAPK signalling. We will first discuss the extensive
number of negative feedback loops targeting the different
components of the ERK1/2 MAPK cascade, specifically
the direct posttranslational modification of pathway components
by downstream protein kinases and the induction
of de novo gene synthesis of specific pathway inhibitors.
We will then evaluate how negative feedback modulates
the spatiotemporal signalling dynamics of the ERK1/2
pathway regarding signalling amplitude and duration as
well as subcellular localisation. Aberrant ERK1/2 activation
results in deregulated proliferation and malignant
transformation in model systems and is commonly
observed in human tumours. Inhibition of the ERK1/2
pathway thus represents an attractive target for the treatment
of malignant tumours with increased ERK1/2
activity. We will, therefore, discuss the effect of ERK1/2
MAPK feedback regulation on cancer treatment and how it
contributes to reduced clinical efficacy of therapeutic
agents and the development of drug resistance | Negative feedback regulation of the ERK1/2 MAPK pathway | negative feedback regulation of the erk1/2 mapk pathway | yesthe extracellular regulated mitogen mapk signalling regulates proliferation transformation. reliably convert stimuli adapt circumstances signalling cell. evolved role. examine mapk signalling. extensive loops targeting mapk cascade posttranslational modification downstream kinases novo inhibitors. modulates spatiotemporal signalling signalling subcellular localisation. aberrant deregulated proliferation malignant commonly tumours. attractive malignant tumours activity. mapk contributes efficacy therapeutic | non_dup | [] |
77414125 | 10.1007/s00018-016-2306-y | Research in the last decade has shown that hematopoietic stem cells (HSCs) interact with and are modulated by a complex multicellular microenvironment in the bone marrow, which includes both the HSC progeny and multiple non-hematopoietic cell types. Intense work is gradually throwing light on the composition of the HSC niche and the molecular cues exchanged between its components, which has implications for HSC production, maintenance and expansion. In addition, it has become apparent that bidirectional interactions between leukemic cells and their niche play a previously unrecognized role in the initiation and development of hematological malignancies. Consequently, targeting of the malignant niche holds considerable promise for more specific antileukemic therapies. Here we summarize the latest insights into HSC niche biology and recent work showing multiple connections between hematological malignancy and alterations in the bone marrow microenvironment.This work was supported by core support grants from the Wellcome Trust and MRC to the Cambridge Stem Cell Institute, the Spanish Ministry of Economy and Competitiveness (SAF-2011-30308), Pro-CNIC Foundation, Severo Ochoa Center of Excellence award SEV-2015-0505 to CNIC, TerCel (Spanish Cell Therapy Network), Ramón y Cajal Program grants RYC-2011-09726 to AS-A and RYC-2009-04703 to SM-F), Marie Curie Career Integration Program grants (FP7-PEOPLE-2011-RG-294262/294096) to AS-A and SM-F; and a ConSEPOC-Comunidad de Madrid grant (S2010/BMD-2542) and Horizon2020 (ERC-2014-CoG-64765 grant to SM-F. This research was partly funded by a European Hematology Association Research Fellowship awarded to AS-A and an International Early Career Scientist Grant from the Howard Hughes Medical Institute to SM-F.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00018-016-2306- | The hematopoietic stem-cell niche in health and leukemia | the hematopoietic stem-cell niche in health and leukemia | decade hematopoietic hscs interact modulated multicellular microenvironment marrow progeny hematopoietic types. intense gradually throwing niche cues exchanged maintenance expansion. apparent bidirectional leukemic niche unrecognized initiation hematological malignancies. targeting malignant niche considerable promise antileukemic therapies. summarize latest insights niche connections hematological malignancy alterations marrow microenvironment.this grants wellcome trust spanish ministry economy competitiveness cnic foundation severo ochoa excellence award cnic tercel spanish ramón cajal grants marie curie career grants consepoc comunidad madrid horizon partly funded hematology fellowship awarded career scientist howard hughes f.this article. appeared springer | non_dup | [] |
83622129 | 10.1007/s00018-016-2316-9 | Contains fulltext :
169248.pdf (publisher's version ) (Open Access)Diabetes strongly predisposes to cardiovascular disease (CVD), the leading cause of mortality in these patients, as well as in the entire population. Hyperglycemia is an important cardiovascular risk factor as shown by the observation that even transient periods of hyperglycemia, despite return to normoglycemia during follow-up, increase the risk for CVD, a phenomenon termed 'hyperglycemic memory'. The molecular mechanisms underlying this phenomenon remain largely unknown. As inflammation plays an important role in the pathogenesis of atherosclerosis, we propose that long-term functional reprogramming of monocytes and macrophages, induced by hyperglycemia, plays an important role in the phenomenon of hyperglycemic memory leading to cardiovascular complications in patients with diabetes. In this review, we discuss recent insights showing that innate immune cells possess the capacity to reprogram their function through epigenetically mediated rewiring of gene transcription, a process termed 'trained immunity'. The long-term reprogramming of monocytes can be induced by microbial as well as metabolic products, and involves a shift in cellular metabolism from oxidative phosphorylation to aerobic glycolysis. We hypothesize that hyperglycemia in diabetes patients induces long-term activation of monocytes and macrophages through similar mechanisms, thereby contributing to plaque development and subsequent macrovascular complications | Diabetes propels the risk for cardiovascular disease: sweet monocytes becoming aggressive? | diabetes propels the risk for cardiovascular disease: sweet monocytes becoming aggressive? | fulltext .pdf publisher predisposes cardiovascular population. hyperglycemia cardiovascular transient hyperglycemia return normoglycemia phenomenon termed hyperglycemic phenomenon largely unknown. inflammation plays pathogenesis atherosclerosis propose reprogramming monocytes macrophages hyperglycemia plays phenomenon hyperglycemic cardiovascular complications diabetes. insights innate immune possess reprogram epigenetically rewiring termed trained immunity reprogramming monocytes microbial metabolic involves metabolism oxidative phosphorylation aerobic glycolysis. hypothesize hyperglycemia induces monocytes macrophages thereby contributing plaque macrovascular complications | non_dup | [] |
78547206 | 10.1007/s00018-016-2397-5 | Altres ajuts: La Marató de TV3 (TV3-20141430)Astrocytic excitability relies on cytosolic calcium increases as a key mechanism, whereby astrocytes contribute to synaptic transmission and hence learning and memory. While it is a cornerstone of neurosciences that experiences are remembered, because transmitters activate gene expression in neurons, long-term adaptive astrocyte plasticity has not been described. Here, we investigated whether the transcription factor CREB mediates adaptive plasticity-like phenomena in astrocytes. We found that activation of CREB-dependent transcription reduced the calcium responses induced by ATP, noradrenaline, or endothelin-1. As to the mechanism, expression of VP16-CREB, a constitutively active CREB mutant, had no effect on basal cytosolic calcium levels, extracellular calcium entry, or calcium mobilization from lysosomal-related acidic stores. Rather, VP16-CREB upregulated sigma-1 receptor expression thereby increasing the release of calcium from the endoplasmic reticulum and its uptake by mitochondria. Sigma-1 receptor was also upregulated in vivo upon VP16-CREB expression in astrocytes. We conclude that CREB decreases astrocyte responsiveness by increasing calcium signalling at the endoplasmic reticulum-mitochondria interface, which might be an astrocyte-based form of long-term depression | CREB decreases astrocytic excitability by modifying subcellular calcium fluxes via the sigma-1 receptor | creb decreases astrocytic excitability by modifying subcellular calcium fluxes via the sigma-1 receptor | altres ajuts marató astrocytic excitability relies cytosolic calcium whereby astrocytes synaptic memory. cornerstone neurosciences experiences remembered transmitters activate adaptive astrocyte plasticity described. creb mediates adaptive plasticity phenomena astrocytes. creb calcium noradrenaline endothelin creb constitutively creb basal cytosolic calcium extracellular calcium entry calcium mobilization lysosomal acidic stores. creb upregulated sigma thereby calcium endoplasmic reticulum uptake mitochondria. sigma upregulated creb astrocytes. creb astrocyte responsiveness calcium signalling endoplasmic reticulum mitochondria astrocyte depression | non_dup | [] |
76999547 | 10.1007/s00018-016-2406-8 | Hydrogen sulfide (H2S) has profound biological effects within living organisms and is now increasingly being considered alongside other gaseous signalling molecules, such as nitric oxide (NO) and carbon monoxide (CO). Conventional use of pharmacological and molecular approaches has spawned a rapidly growing research field that has identified H2S as playing a functional role in cell-signalling and post-translational modifications. Recently, a number of laboratories have reported the use of siRNA methodologies and genetic mouse models to mimic the loss of function of genes involved in the biosynthesis and degradation of H2S within tissues. Studies utilising these systems are revealing new insights into the biology of H2S within the cardiovascular system, inflammatory disease, and in cell signalling. In light of this work, the current review will describe recent advances in H2S research made possible by the use of molecular approaches and genetic mouse models with perturbed capacities to generate or detoxify physiological levels of H2S gas within tissue | H2S biosynthesis and catabolism: new insights from molecular studies | h2s biosynthesis and catabolism: new insights from molecular studies | sulfide profound living organisms increasingly alongside gaseous signalling nitric oxide monoxide pharmacological spawned rapidly growing playing signalling translational modifications. laboratories sirna methodologies mimic biosynthesis degradation tissues. utilising revealing insights cardiovascular inflammatory signalling. advances perturbed capacities detoxify physiological | non_dup | [] |
153533728 | 10.1007/s00018-016-2423-7 | Background: Viral myocarditis can severely damage the myocardium through excessive infiltration of immune cells. Osteoglycin (OGN) is part of the small leucine-rich repeat proteoglycan (SLRP) family. SLRP’s may affect inflammatory and fibrotic processes, but the implication of OGN in cardiac inflammation and the resulting injury upon viral myocarditis is unknown. Methods and results: This study uncovered a previously unidentified 72-kDa variant of OGN that is predominant in cardiac human and mouse samples of viral myocarditis. Its absence in mice significantly decreased cardiac inflammation and injury in Coxsackievirus-B3-induced myocarditis. It also delayed mortality in lipopolysaccharide-induced endotoxemia going along with a reduced systemic production of pro-inflammatory cytokines. This 72-kDa OGN is expressed in the cell membrane of circulating and resident cardiac macrophages and neutrophils. Co-immunoprecipitation and OGN siRNA experiments revealed that this 72-kDa variant activates the toll-like receptor-4 (TLR4) with a concomitant increase in IL-6, TNF-α, IL-1β, and IL-12 expression. This immune cell activation by OGN occurred via MyD88 and increased phosphorylation of c-jun. Finally, the 72-kDa chondroitin sulfate is the result of O-linked glycosylation of the 32-kDa protein core of OGN. In contrast, the 34-kDa dermatan sulfate-OGN, involved in collagen cross linking, was also the result of O-linked glycosylation. Conclusion: The current study discovered a novel 72-kDa chondroitin sulfate-OGN that is specific for innate immune cells. This variant is able to bind and activate TLR4. The absence of OGN decreases cytokine production by both circulating and cardiac leukocytes upon (systemic) LPS exposure, and reduces cardiac inflammation and injury in viral myocarditis | A novel 72-kDa leukocyte-derived osteoglycin enhances the activation of toll-like receptor 4 and exacerbates cardiac inflammation during viral myocarditis | a novel 72-kda leukocyte-derived osteoglycin enhances the activation of toll-like receptor 4 and exacerbates cardiac inflammation during viral myocarditis | viral myocarditis severely myocardium excessive infiltration immune cells. osteoglycin leucine repeat proteoglycan slrp family. slrp’s inflammatory fibrotic implication inflammation injury viral myocarditis unknown. uncovered unidentified variant predominant viral myocarditis. inflammation injury coxsackievirus myocarditis. delayed lipopolysaccharide endotoxemia going systemic inflammatory cytokines. circulating resident macrophages neutrophils. immunoprecipitation sirna variant activates toll concomitant expression. immune occurred phosphorylation jun. chondroitin sulfate glycosylation ogn. dermatan sulfate collagen linking glycosylation. discovered chondroitin sulfate innate immune cells. variant bind activate cytokine circulating leukocytes systemic reduces inflammation injury viral myocarditis | non_dup | [] |
84040233 | 10.1007/s00018-016-2441-5 | Retraction of mesenchymal stromal cells supports the invasion of colorectal cancer cells (CRC) into the adjacent compartment. CRC-secreted 12(S)-HETE enhances the retraction of cancer-associated fibroblasts (CAFs) and therefore, 12(S)-HETE may enforce invasivity of CRC. Understanding the mechanisms of metastatic CRC is crucial for successful intervention. Therefore, we studied pro-invasive contributions of stromal cells in physiologically relevant three-dimensional in vitro assays consisting of CRC spheroids, CAFs, extracellular matrix and endothelial cells, as well as in reductionist models. In order to elucidate how CAFs support CRC invasion, tumour spheroid-induced CAF retraction and free intracellular Ca2+ levels were measured and pharmacological-or siRNA-based inhibition of selected signalling cascades was performed. CRC spheroids caused the retraction of CAFs, generating entry gates in the adjacent surrogate stroma. The responsible trigger factor 12(S)-HETE provoked a signal, which was transduced by PLC, IP3, free intracellular Ca2+, Ca(2+)calmodulin-kinase-II, RHO/ROCK and MYLK which led to the activation of myosin light chain 2, and subsequent CAF mobility. RHO activity was observed downstream as well as upstream of Ca2+ release. Thus, Ca2+ signalling served as central signal amplifier. Treatment with the FDA-approved drugs carbamazepine, cinnarizine, nifedipine and bepridil HCl, which reportedly interfere with cellular calcium availability, inhibited CAF-retraction. The elucidation of signalling pathways and identification of approved inhibitory drugs warrant development of intervention strategies targeting tumour-stroma interaction | Colon cancer cell-derived 12(S)-HETE induces the retraction of cancer-associated fibroblast via MLC2, RHO/ROCK and Ca2+ signalling | colon cancer cell-derived 12(s)-hete induces the retraction of cancer-associated fibroblast via mlc2, rho/rock and ca2+ signalling | retraction mesenchymal stromal supports invasion colorectal adjacent compartment. secreted hete enhances retraction fibroblasts cafs hete enforce invasivity crc. metastatic crucial successful intervention. invasive stromal physiologically assays consisting spheroids cafs extracellular endothelial reductionist models. elucidate cafs invasion tumour spheroid retraction intracellular pharmacological sirna signalling cascades performed. spheroids retraction cafs generating entry gates adjacent surrogate stroma. trigger hete provoked transduced intracellular calmodulin rock mylk myosin mobility. downstream upstream release. signalling served amplifier. approved drugs carbamazepine cinnarizine nifedipine bepridil reportedly interfere calcium availability inhibited retraction. elucidation signalling pathways approved inhibitory drugs warrant targeting tumour stroma | non_dup | [] |
94541882 | 10.1007/s00018-017-2516-y | Adaptive immunity critically contributes to control acute infection with enteropathogenic Yersinia pseudotuberculosis; however, the role of CD4(+) T cell subsets in establishing infection and allowing pathogen persistence remains elusive. Here, we assessed the modulatory capacity of Y. pseudotuberculosis on CD4(+) T cell differentiation. Using in vivo assays, we report that infection with Y. pseudotuberculosis resulted in enhanced priming of IL-17-producing T cells (Th17 cells), whereas induction of Foxp3(+) regulatory T cells (Tregs) was severely disrupted in gut-draining mesenteric lymph nodes (mLNs), in line with altered frequencies of tolerogenic and proinflammatory dendritic cell (DC) subsets within mLNs. Additionally, by using a DC-free in vitro system, we could demonstrate that Y. pseudotuberculosis can directly modulate T cell receptor (TCR) downstream signaling within naïve CD4(+) T cells and Tregs via injection of effector molecules through the type III secretion system, thereby affecting their functional properties. Importantly, modulation of naïve CD4(+) T cells by Y. pseudotuberculosis resulted in an enhanced Th17 differentiation and decreased induction of Foxp3(+) Tregs in vitro. These findings shed light to the adjustment of the Th17-Treg axis in response to acute Y. pseudotuberculosis infection and highlight the direct modulation of CD4(+) T cell subsets by altering their TCR downstream signaling | Yersinia pseudotuberculosis supports Th17 differentiation and limits de novo regulatory T cell induction by directly interfering with T cell receptor signaling. | yersinia pseudotuberculosis supports th17 differentiation and limits de novo regulatory t cell induction by directly interfering with t cell receptor signaling. | adaptive immunity critically contributes enteropathogenic yersinia pseudotuberculosis subsets establishing allowing pathogen persistence elusive. modulatory pseudotuberculosis differentiation. assays pseudotuberculosis resulted priming producing foxp regulatory tregs severely disrupted draining mesenteric lymph mlns altered tolerogenic proinflammatory dendritic subsets mlns. additionally pseudotuberculosis modulate downstream naïve tregs injection effector secretion thereby affecting properties. importantly modulation naïve pseudotuberculosis resulted foxp tregs vitro. shed adjustment treg pseudotuberculosis highlight modulation subsets altering downstream | non_dup | [] |
143977359 | 10.1007/s00018-017-2600-3 | Retinoic acid (RA) is of major importance during vertebrate embryonic development and its levels need to be strictly regulated otherwise congenital malformations will develop. Through the action of specific nuclear receptors, named RAR/RXR, RA regulates the expression of genes that eventually influence proliferation and tissue patterning. RA has been described as crucial for different stages of mammalian lung morphogenesis, and as part of a complex molecular network that contributes to precise organogenesis; nonetheless, nothing is known about its role in avian lung development. The current report characterizes, for the first time, the expression pattern of RA signaling members (stra6, raldh2, raldh3, cyp26a1, rar alpha, and rar beta) and potential RA downstream targets (sox2, sox9, meis1, meis2, tgf beta 2, and id2) by in situ hybridization. In the attempt of unveiling the role of RA in chick lung branching, in vitro lung explants were performed. Supplementation studies revealed that RA stimulates lung branching in a dose-dependent manner. Moreover, the expression levels of cyp26a1, sox2, sox9, rar beta, meis2, hoxb5, tgf beta 2, id2, fgf10, fgfr2, and shh were evaluated after RA treatment to disclose a putative molecular network underlying RA effect. In situ hybridization analysis showed that RA is able to alter cyp26a1, sox9, tgf beta 2, and id2 spatial distribution; to increase rar beta, meis2, and hoxb5 expression levels; and has a very modest effect on sox2, fgf10, fgfr2, and shh expression levels. Overall, these findings support a role for RA in the proximal-distal patterning and branching morphogenesis of the avian lung and reveal intricate molecular interactions that ultimately orchestrate branching morphogenesis.The authors would like to thank Ana Lima
for slide sectioning and Rita Lopes for contributing to the initiation
of this project. This work has been funded by FEDER funds,
through the Competitiveness Factors Operational Programme
(COMPETE), and by National funds, through the Foundation for
Science and Technology (FCT), under the scope of the Project
POCI-01-0145-FEDER-007038; and by the Project NORTE-01-0145-
FEDER-000013, supported by the Northern Portugal Regional Operational
Programme (NORTE 2020), under the Portugal 2020 Partnership
Agreement, through the European Regional Development Fund
(FEDER). The funders had no role in study design, data collection
and analysis, decision to publish, or preparation of the manuscript.info:eu-repo/semantics/publishedVersio | Retinoic acid regulates avian lung branching through a molecular network | retinoic acid regulates avian lung branching through a molecular network | retinoic vertebrate embryonic strictly regulated congenital malformations develop. receptors named regulates eventually proliferation patterning. crucial mammalian morphogenesis contributes precise organogenesis nonetheless nothing avian development. characterizes stra raldh raldh alpha beta downstream targets meis meis beta situ hybridization. attempt unveiling chick branching explants performed. supplementation stimulates branching manner. beta meis hoxb beta fgfr disclose putative effect. situ hybridization alter beta beta meis hoxb modest fgfr levels. proximal distal patterning branching morphogenesis avian reveal intricate ultimately orchestrate branching morphogenesis.the lima slide sectioning rita lopes contributing initiation project. funded feder funds competitiveness operational programme compete funds foundation scope poci feder norte feder northern portugal operational programme norte portugal partnership fund feder info repo semantics publishedversio | non_dup | [] |
132263279 | 10.1007/s00018-017-2654-2 | This is the final version of the article. Available from Springer Verlag via the DOI in this record.Wnt growth factors regulate one of the most important signaling networks during development, tissue homeostasis and disease. Despite the biological importance of Wnt signaling, the mechanism of endocytosis during this process is ill described. Wnt molecules can act as paracrine signals, which are secreted from the producing cells and transported through neighboring tissue to activate signaling in target cells. Endocytosis of the ligand is important at several stages of action: One central function of endocytic trafficking in the Wnt pathway occurs in the source cell. Furthermore, the β-catenin-dependent Wnt ligands require endocytosis for signal activation and to regulate gene transcription in the responding cells. Alternatively, Wnt/β-catenin-independent signaling regulates endocytosis of cell adherence plaques to control cell migration. In this comparative review, we elucidate these three fundamental interconnected functions, which together regulate cellular fate and cellular behavior. Based on established hypotheses and recent findings, we develop a revised picture for the complex function of endocytosis in the Wnt signaling network.Funding was provided by Deutsche Forschungsgemeinschaft (Grant no. SCHO847-5) and the University of Exeter (GB) (LSI Start-up Grant) | The function of endocytosis in Wnt signaling | the function of endocytosis in wnt signaling | article. springer verlag record.wnt regulate homeostasis disease. endocytosis described. paracrine secreted producing transported neighboring activate cells. endocytosis ligand endocytic trafficking cell. catenin ligands endocytosis regulate responding cells. alternatively catenin regulates endocytosis adherence plaques migration. comparative elucidate interconnected regulate fate behavior. hypotheses revised picture endocytosis network.funding deutsche forschungsgemeinschaft scho exeter | non_dup | [] |
156892999 | 10.1007/s00018-017-2716-5 | An important trait associated with the salt tolerance of wheat is the exclusion of sodium ions ( Na⁺) from the shoot. We have previously shown that the sodium transporters TmHKT1;5-A and TaHKT1;5-D, from Triticum monoccocum (Tm) and Triticum aestivum (Ta), are encoded by genes underlying the major shoot Na⁺- exclusion loci Nax1 and Kna1, respectively. Here, using heterologous expression, we show that the affinity (Km) for the Na⁺ transport of TmHKT1;5-A, at 2.66 mM, is higher than that of TaHKT1;5-D at 7.50 mM. Through 3D structural modelling, we identify residues D⁴⁷¹/a gap and D⁴⁷⁴/ G⁴⁷³ that contribute to this property. We identify four additional mutations in amino acid residues that inhibit the transport activity of TmHKT1;5-A, which are predicted to be the result of an occlusion of the pore. We propose that the underlying transport properties of TmHKT1;5-A and TaHKT1;5-D contribute to their unique ability to improve Na⁺ exclusion in wheat that leads to an improved salinity tolerance in the field.Bo Xu, Shane Waters, Caitlin S. Byrt, Darren Plett, Stephen D. Tyerman, Mark Tester, Rana Munns, Maria Hrmova, Matthew Gilliha | Structural variations in wheat HKT1;5 underpin differences in Na+ transport capacity | structural variations in wheat hkt1;5 underpin differences in na+ transport capacity | trait salt tolerance wheat exclusion sodium shoot. sodium transporters tmhkt tahkt triticum monoccocum triticum aestivum encoded shoot exclusion loci respectively. heterologous affinity tmhkt tahkt d⁴⁷¹ d⁴⁷⁴ g⁴⁷³ property. inhibit tmhkt occlusion pore. propose tmhkt tahkt exclusion wheat salinity tolerance field.bo shane waters caitlin byrt darren plett stephen tyerman mark tester rana munns maria hrmova matthew gilliha | non_dup | [] |
154965917 | 10.1007/s00018-017-2743-2 | Proteins routed to the secretory pathway start their journey by being transported across biological membranes, such as the endoplasmic reticulum. The essential nature of this protein translocation process has led to the evolution of several factors that specifically target the translocon and block translocation. In this review, various translocation pathways are discussed together with known inhibitors of translocation. Properties of signal peptide-specific systems are highlighted for the development of new therapeutic and antimicrobial applications, as compounds can target signal peptides from either host cells or pathogens and thereby selectively prevent translocation of those specific proteins. Broad inhibition of translocation is also an interesting target for the development of new anticancer drugs because cancer cells heavily depend on efficient protein translocation into the endoplasmic reticulum to support their fast growth.status: publishe | Inhibitors of protein translocation across membranes of the secretory pathway: novel antimicrobial and anticancer agents | inhibitors of protein translocation across membranes of the secretory pathway: novel antimicrobial and anticancer agents | routed secretory journey transported membranes endoplasmic reticulum. translocation translocon translocation. translocation pathways inhibitors translocation. highlighted therapeutic antimicrobial peptides pathogens thereby selectively prevent translocation proteins. broad translocation anticancer drugs heavily translocation endoplasmic reticulum growth.status publishe | non_dup | [] |
154082317 | 10.1007/s00018-018-2784-1 | In the last decade, metabolism has been recognized as a major determinant of immunological processes. During an inflammatory response, macrophages undergo striking changes in their metabolism. This metabolic reprogramming is governed by a complex interplay between metabolic enzymes and metabolites of different pathways and represents the basis for proper macrophage function. It is now evident that these changes go far beyond the well-known Warburg effect and the perturbation of metabolic targets is being investigated as a means to treat infections and auto-immune diseases. In the present review, we will aim to provide an overview of the metabolic responses during proinflammatory macrophage activation and show how these changes modulate the immune response | Biochemistry of proinflammatory macrophage activation. | biochemistry of proinflammatory macrophage activation. | decade metabolism recognized determinant immunological processes. inflammatory macrophages undergo striking metabolism. metabolic reprogramming governed interplay metabolic enzymes metabolites pathways proper macrophage function. evident warburg perturbation metabolic targets treat infections auto immune diseases. overview metabolic proinflammatory macrophage modulate immune | non_dup | [] |
158600378 | 10.1007/s00018-018-2848-2 | Ubiquitination, the covalent attachment of ubiquitin to proteins, by E3 ligases of the HECT (homologous to E6AP C terminus) family is critical in controlling diverse physiological pathways. Stringent control of HECT E3 ligase activity and substrate specificity is essential for cellular health, whereas deregulation of HECT E3s plays a prominent role in disease. The cell employs a wide variety of regulatory mechanisms to control HECT E3 activity and substrate specificity. Here, we summarize the current understanding of these regulatory mechanisms that control HECT E3 function. Substrate specificity is generally determined by interactions of adaptor proteins with domains in the N-terminal extensions of HECT E3 ligases. These N-terminal domains have also been found to interact with the HECT domain, resulting in the formation of inhibitory conformations. In addition, catalytic activity of the HECT domain is commonly regulated at the level of E2 recruitment and through HECT E3 oligomerization. The previously mentioned regulatory mechanisms can be controlled through protein–protein interactions, post-translational modifications, the binding of calcium ions, and more. Functional activity is determined not only by substrate recruitment and catalytic activity, but also by the type of ubiquitin polymers catalyzed to the substrate. While this is often determined by the specific HECT member, recent studies demonstrate that HECT E3s can be modulated to alter the type of ubiquitin polymers they catalyze. Insight into these diverse regulatory mechanisms that control HECT E3 activity may open up new avenues for therapeutic strategies aimed at inhibition or enhancement of HECT E3 function in disease-related pathways | Regulating the human HECT E3 ligases | regulating the human hect e3 ligases | ubiquitination covalent attachment ubiquitin ligases hect homologous terminus controlling diverse physiological pathways. stringent hect ligase specificity deregulation hect plays prominent disease. employs regulatory hect specificity. summarize regulatory hect function. specificity adaptor extensions hect ligases. interact hect inhibitory conformations. catalytic hect commonly regulated recruitment hect oligomerization. regulatory protein–protein translational modifications calcium more. recruitment catalytic ubiquitin polymers catalyzed substrate. hect member hect modulated alter ubiquitin polymers catalyze. insight diverse regulatory hect avenues therapeutic aimed enhancement hect pathways | non_dup | [] |
162564039 | 10.1007/s00018-018-2886-9 | Once viewed as a passive physiological state, sleep is a heterogeneous and complex sequence of brain states with essential efects on synaptic plasticity and neuronal functioning. Rapid-eye-movement (REM) sleep has been shown to promote calcium-dependent plasticity in principal neurons of the cerebral cortex, both during memory consolidation in adults and during post-natal development. This article reviews the plasticity mechanisms triggered by REM sleep, with a focus on the emerging role of kinases and immediate-early genes for the progressive corticalization of hippocampus-dependent memories. The body of evidence suggests that memory corticalization triggered by REM sleep is a systemic phenomenon with cellular and molecular causes | Memory corticalization triggered by?REM sleep: mechanisms of?cellular and?systems consolidation | memory corticalization triggered by?rem sleep: mechanisms of?cellular and?systems consolidation | viewed passive physiological sleep heterogeneous efects synaptic plasticity neuronal functioning. movement sleep promote calcium plasticity principal cerebral cortex consolidation adults natal development. reviews plasticity triggered sleep emerging kinases immediate progressive corticalization hippocampus memories. corticalization triggered sleep systemic phenomenon | non_dup | [] |
162051026 | 10.1007/s00018-018-2950-5 | Hearing loss is a common affection mainly resulting from irreversible loss of the sensory hair cells of the cochlea; therefore, developing therapies to replace missing hair cells is essential. Understanding the mechanisms that drive their formation will not only help to unravel the molecular basis of deafness, but also give a roadmap for recapitulating hair cells development from cultured pluripotent stem cells. In this review, we provide an overview of the molecular mechanisms involved in hair cell production from both human and mouse embryonic stem cells. We then provide insights how this knowledge has been applied to differentiate induced pluripotent stem cells into otic progenitors and hair cells. Finally, we discuss the current limitations for properly obtaining functional hair cell in a Petri dish, as well as the difficulties that have to be overcome prior to consider stem cell therapy as a potential treatment for hearing loss.Peer reviewe | Pluripotent stem cell-derived cochlear cells: a challenge in constant progress | pluripotent stem cell-derived cochlear cells: a challenge in constant progress | hearing affection irreversible sensory hair cochlea therapies replace missing hair essential. drive unravel deafness roadmap recapitulating hair cultured pluripotent cells. overview hair embryonic cells. insights differentiate pluripotent otic progenitors hair cells. limitations properly obtaining hair petri dish difficulties overcome hearing loss.peer reviewe | non_dup | [] |
2574851 | 10.1007/s00020-003-1279-z | We revisit the computation of (2-modified) Fredholm determinants for
operators with matrix-valued semi-separable integral kernels. The latter occur,
for instance, in the form of Green's functions associated with closed ordinary
differential operators on arbitrary intervals on the real line. Our approach
determines the (2-modified) Fredholm determinants in terms of solutions of
closely associated Volterra integral equations, and as a result offers a
natural way to compute such determinants.
We illustrate our approach by identifying classical objects such as the Jost
function for half-line Schr\"odinger operators and the inverse transmission
coefficient for Schr\"odinger operators on the real line as Fredholm
determinants, and rederiving the well-known expressions for them in due course.
We also apply our formalism to Floquet theory of Schr\"odinger operators, and
upon identifying the connection between the Floquet discriminant and underlying
Fredholm determinants, we derive new representations of the Floquet
discriminant.
Finally, we rederive the explicit formula for the 2-modified Fredholm
determinant corresponding to a convolution integral operator, whose kernel is
associated with a symbol given by a rational function, in a straghtforward
manner. This determinant formula represents a Wiener-Hopf analog of Day's
formula for the determinant associated with finite Toeplitz matrices generated
by the Laurent expansion of a rational function.Comment: LaTeX, 37 page | (Modified) Fredholm Determinants for Operators with Matrix-Valued
Semi-Separable Integral Kernels Revisited | (modified) fredholm determinants for operators with matrix-valued semi-separable integral kernels revisited | revisit fredholm determinants valued separable kernels. ordinary intervals line. determines fredholm determinants closely volterra offers determinants. illustrate identifying jost schr odinger schr odinger fredholm determinants rederiving expressions course. formalism floquet schr odinger identifying connection floquet discriminant fredholm determinants derive representations floquet discriminant. rederive fredholm determinant convolution kernel symbol rational straghtforward manner. determinant wiener hopf analog determinant toeplitz laurent rational latex | non_dup | [] |
1918733 | 10.1007/s00020-007-1480-6 | Gohm, Rolf; Dey, S., 'Characteristic function for ergodic tuples', Integral Equations and Operator Theory 58(1) pp.43-63 RAE2008Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G. Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed.preprintpreprintPeer reviewe | Characteristic Functions for Ergodic Tuples | characteristic functions for ergodic tuples | gohm rolf ergodic tuples motivated markov dilations notion ergodic coisometric contractions subspace adjoints. extends popescu. unitary tuples computed.preprintpreprintpeer reviewe | non_dup | [] |
1935277 | 10.1007/s00020-007-1534-9 | We present several results associated to a holomorphic-interpolation problem
for the spectral unit ball \Omega_n, n\geq 2. We begin by showing that a known
necessary condition for the existence of a
$\mathcal{O}(D;\Omega_n)$-interpolant (D here being the unit disc in the
complex plane), given that the matricial data are non-derogatory, is not
sufficient. We provide next a new necessary condition for the solvability of
the two-point interpolation problem -- one which is not restricted only to
non-derogatory data, and which incorporates the Jordan structure of the
prescribed data. We then use some of the ideas used in deducing the latter
result to prove a Schwarz-type lemma for holomorphic self-maps of \Omega_n,
n\geq 2.Comment: Added a definition (Def.1.1); 2 of the 4 results herein are minor
refinements of those in the author's preprint math.CV/0608177; to appear in
Integral Eqns. Operator Theor | Some new observations on interpolation in the spectral unit ball | some new observations on interpolation in the spectral unit ball | holomorphic interpolation ball omega begin mathcal omega interpolant disc matricial derogatory sufficient. solvability interpolation restricted derogatory incorporates jordan prescribed data. ideas deducing schwarz holomorphic omega def. herein minor refinements preprint math.cv eqns. theor | non_dup | [] |
158836896 | 10.1007/s00020-008-1569-6 | We find a description of the restriction of doubly stochastic maps to separable abelian C ∗ -subalgebras of a II1 factor M. We use this local form of doubly stochastic maps to develop a notion of joint majorization between ntuples of mutually commuting self-adjoint operators that extends those of Kamei (for single self-adjoint operators) and Hiai (for single normal operators) in the II1 factor case. Several characterizations of this joint majorization are obtained. As a byproduct we prove that any separable abelian C ∗ -subalgebra of M can be embedded into a separable abelian C ∗ -subalgebra of M with diffuse spectral measure.Fil: Argerami, Martin. University of Regina; CanadáFil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentin | The local form of doubly stochastic maps and joint majorization in II1 factors | the local form of doubly stochastic maps and joint majorization in ii1 factors | restriction doubly stochastic separable abelian subalgebras doubly stochastic notion majorization ntuples mutually commuting adjoint extends kamei adjoint hiai case. characterizations majorization obtained. byproduct separable abelian subalgebra embedded separable abelian subalgebra diffuse measure.fil argerami martin. regina canadáfil massey pedro gustavo. universidad nacional plata. facultad ciencias exactas. departamento matematicas argentina. consejo nacional investigaciones científicas técnicas. oficina coordinación administrativa saavedra instituto argentino matemática alberto calderon argentin | non_dup | [] |
2016989 | 10.1007/s00020-008-1571-z | For $a,\alpha>0$ let $E(a,\alpha)$ be the set of all compact operators $A$ on
a separable Hilbert space such that $s_n(A)=O(\exp(-an^\alpha))$, where
$s_n(A)$ denotes the $n$-th singular number of $A$. We provide upper bounds for
the norm of the resolvent $(zI-A)^{-1}$ of $A$ in terms of a quantity
describing the departure from normality of $A$ and the distance of $z$ to the
spectrum of $A$. As a consequence we obtain upper bounds for the Hausdorff
distance of the spectra of two operators in $E(a,\alpha)$.Comment: AMS-LaTeX, 20 page | Resolvent estimates for operators belonging to exponential classes | resolvent estimates for operators belonging to exponential classes | alpha alpha separable hilbert alpha singular bounds norm resolvent quantity describing departure normality bounds hausdorff alpha .comment latex | non_dup | [] |
1949521 | 10.1007/s00020-008-1634-1 | We introduce a planar waveguide of constant width with non-Hermitian
PT-symmetric Robin boundary conditions. We study the spectrum of this system in
the regime when the boundary coupling function is a compactly supported
perturbation of a homogeneous coupling. We prove that the essential spectrum is
positive and independent of such perturbation, and that the residual spectrum
is empty. Assuming that the perturbation is small in the supremum norm, we show
that it gives rise to real weakly-coupled eigenvalues converging to the
threshold of the essential spectrum. We derive sufficient conditions for these
eigenvalues to exist or to be absent. Moreover, we construct the leading terms
of the asymptotic expansions of these eigenvalues and the associated
eigenfunctions.Comment: LaTeX, 25 pages; more detailed description of various types of
spectra; version accepted for publication in Integral Equations Operator
Theor | PT-symmetric waveguides | pt-symmetric waveguides | planar waveguide hermitian robin conditions. compactly perturbation homogeneous coupling. perturbation residual empty. perturbation supremum norm weakly eigenvalues converging spectrum. derive eigenvalues absent. asymptotic expansions eigenvalues latex pages publication theor | non_dup | [] |
2095404 | 10.1007/s00020-010-1802-y | In this paper we extend a method of Arveson and McCullough to prove a
tangential interpolation theorem for subalgebras of $H^\infty$. This tangential
interpolation result implies a Toelitz corona theorem. In particular, it is
shown that the set of matrix positivity conditions is indexed by cyclic
subspaces, which is analogous to the results obtained for the ball and the
polydisk algebra by Trent-Wick and Douglas-Sarkar.Comment: 17 pages, no figures, to appear in Integral Equations and Operator
Theor | Duality, Tangential Interpolation, and Toeplitz Corona Problems | duality, tangential interpolation, and toeplitz corona problems | extend arveson mccullough tangential interpolation subalgebras infty tangential interpolation toelitz corona theorem. positivity indexed cyclic subspaces analogous ball polydisk trent wick douglas pages theor | non_dup | [] |
2120465 | 10.1007/s00020-010-1814-7 | Multipliers have been recently introduced as operators for Bessel sequences
and frames in Hilbert spaces. These operators are defined by a fixed
multiplication pattern (the symbol) which is inserted between the analysis and
synthesis operators. In this paper, we will generalize the concept of Bessel
multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be
shown that bounded symbols lead to bounded operators. Symbols converging to
zero induce compact operators. Furthermore, we will give sufficient conditions
for multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.Comment: 17 page | Multipliers for p-Bessel sequences in Banach spaces | multipliers for p-bessel sequences in banach spaces | multipliers bessel frames hilbert spaces. multiplication symbol inserted operators. generalize bessel multipliers bessel riesz banach spaces. symbols operators. symbols converging induce operators. multipliers operators. dependency multipliers | non_dup | [] |
2118724 | 10.1007/s00020-010-1831-6 | We study spectral properties of Schr\"odinger operators on $\RR^d$. The
electromagnetic potential is assumed to be determined locally by a colouring of
the lattice points in $\ZZ^d$, with the property that frequencies of finite
patterns are well defined. We prove that the integrated density of states
(spectral distribution function) is approximated by its finite volume
analogues, i.e.the normalised eigenvalue counting functions. The convergence
holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq
p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe | $L^p$-approximation of the integrated density of states for
Schr\"odinger operators with finite local complexity | $l^p$-approximation of the integrated density of states for schr\"odinger operators with finite local complexity | schr odinger electromagnetic locally colouring defined. approximated analogues i.e.the normalised eigenvalue counting functions. infty pages minor fixe | non_dup | [] |
52439045 | 10.1007/s00020-011-1867-2 | International audienceLet A and B be non-negative self-adjoint operators in a separable Hilbert space such that their form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary parameter values in the L 2-norm, that is, one has limn→+∞∫−TT∥∥(e−itA/ne−itB/n)nh−e−itCh∥∥2dt=0 for each element h of the Hilbert space and any T > 0. This result is extended to the class of holomorphic Kato functions, to which the exponential function belongs. Moreover, for a class of admissible functions: ϕ(⋅),ψ(⋅):R+⟶C , where R+:=[0,∞) , satisfying in addition Re(ϕ(y))≥0,Jm(ϕ(y)≤0 and Jm(ψ(y))≤0 for y∈R+ , we prove that \rm s-limn→∞(ϕ(tA/n)ψ(tB/n))n=e−itC holds true uniformly on [0,T]∋t for any T > 0 | Remarks on the Trotter-Kato Product Formula for Unitary Groups | remarks on the trotter-kato product formula for unitary groups | audiencelet adjoint separable hilbert densely defined. trotter imaginary norm limn→ ∞∫−tt∥∥ e−ita ne−itb nh−e−itch∥∥ hilbert holomorphic kato exponential belongs. admissible satisfying limn→∞ e−itc uniformly | non_dup | [] |
2162083 | 10.1007/s00020-011-1882-3 | We give sufficient conditions for essential self-adjointness of magnetic
Schr\"odinger operators on locally finite graphs. Two of the main theorems of
the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as
follows: the ordering of presentation has been modified in several places,
more details have been provided in several places, some notations have been
changed, two examples have been added, and several new references have been
inserted. The final version of this preprint will appear in Integral
Equations and Operator Theor | Essential self-adjointness of magnetic Schr\"odinger operators on
locally finite graphs | essential self-adjointness of magnetic schr\"odinger operators on locally finite graphs | adjointness schr odinger locally graphs. theorems generalize torki pages differs ordering presentation places places notations changed inserted. preprint theor | non_dup | [] |
2090616 | 10.1007/s00020-011-1888-x | We study Laplace-type operators on hybrid manifolds, i.e. on configurations
consisting of closed two-dimensional manifolds and one-dimensional segments.
Such an operator can be constructed by using the Laplace-Beltrami operators on
each component with some boundary conditions at the points of gluing. The large
spectral parameter expansion of the trace of the second power of the resolvent
is obtained. Some questions of the inverse spectral theory are adressed.Comment: To appear in Integral Equations and Operator Theory (2011 | Resolvent expansions on hybrid manifolds | resolvent expansions on hybrid manifolds | laplace hybrid manifolds i.e. configurations consisting manifolds segments. laplace beltrami gluing. trace resolvent obtained. | non_dup | [] |
2081532 | 10.1007/s00020-011-1900-5 | Let $t\mapsto A(t)$ for $t\in T$ be a $C^M$-mapping with values unbounded
operators with compact resolvents and common domain of definition which are
self-adjoint or normal. Here $C^M$ stands for $C^\om$ (real analytic), a
quasianalytic or non-quasianalytic Denjoy-Carleman class, $C^\infty$, or a
H\"older continuity class $C^{0,\al}$. The parameter domain $T$ is either
$\mathbb R$ or $\mathbb R^n$ or an infinite dimensional convenient vector
space. We prove and review results on $C^M$-dependence on $t$ of the
eigenvalues and eigenvectors of $A(t)$.Comment: 8 page | Denjoy-Carleman differentiable perturbation of polynomials and unbounded
operators | denjoy-carleman differentiable perturbation of polynomials and unbounded operators | mapsto unbounded resolvents adjoint normal. stands analytic quasianalytic quasianalytic denjoy carleman infty older continuity mathbb mathbb infinite convenient space. eigenvalues eigenvectors .comment | non_dup | [] |
48224455 | 10.1007/s00020-012-1954-z | International audienceIn this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the boundary. We prove that the boundary integral operators are infinitely differentiable without loss of regularity. The potential operators are infinitely shape differentiable away from the boundary, whereas their derivatives lose regularity near the boundary. We study the shape differentiability of surface differential operators. The shape differentiability properties of the usual strongly singular or hypersingular boundary integral operators of interest in acoustic, elastodynamic or electromagnetic potential theory can then be established by expressing them in terms of integral operators with weakly singular kernels and of surface differential operators | Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators. | shape derivatives of boundary integral operators in electromagnetic scattering. part i: shape differentiability of pseudo-homogeneous boundary integral operators. | audiencein differentiability potentials weakly singular pseudo homogeneous kernels acting sobolev deformations boundary. infinitely differentiable regularity. infinitely differentiable away derivatives lose regularity boundary. differentiability operators. differentiability usual singular hypersingular acoustic elastodynamic electromagnetic expressing weakly singular kernels | non_dup | [] |
48224452 | 10.1007/s00020-012-1955-y | International audienceWe develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. The latter are typically bounded on the space of tangential vector fields of mixed regularity $TH\sp{-\frac{1}{2}}(\Div_{\Gamma},\Gamma)$. Using Helmholtz decomposition, we can base their analysis on the study of pseudo-differential integral operators in standard Sobolev spaces, but we then have to study the Gâteaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity. We also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem | Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle | shape derivatives of boundary integral operators in electromagnetic scattering. part ii : application to scattering by a homogeneous dielectric obstacle | audiencewe harmonic electromagnetic penetrable obstacle. solve electromagnetic differentiability electromagnetic operators. tangential regularity frac gamma gamma helmholtz decomposition pseudo sobolev gâteaux differentiability operators. electromagnetic infinitely differentiable regularity. dielectric electromagnetic | non_dup | [] |
42683848 | 10.1007/s00020-012-1970-z | The Fredholm integral equations of the first kind are a classical example of
ill-posed problem in the sense of Hadamard. If the integral operator is
self-adjoint and admits a set of eigenfunctions, then a formal solution can be
written in terms of eigenfunction expansions. One of the possible methods of
regularization consists in truncating this formal expansion after restricting
the class of admissible solutions through a-priori global bounds. In this paper
we reconsider various possible methods of truncation from the viewpoint of the
$\varepsilon$-coverings of compact sets.Comment: 17 page | Fredholm integral equations of the first kind and topological
information theory | fredholm integral equations of the first kind and topological information theory | fredholm kind posed hadamard. adjoint admits eigenfunctions formal eigenfunction expansions. regularization truncating formal restricting admissible priori bounds. reconsider truncation viewpoint varepsilon coverings | non_dup | [] |
52923967 | 10.1007/s00020-012-2009-1 | Cataloged from PDF version of article.We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of *-semigroups from the point of view of generation of *-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifies many dilation results, in particular B. Sz.-Nagy's and Stinesprings' dilation type theorems. © 2012 Springer Basel | Dilations of some VH-spaces operator valued invariant kernels | dilations of some vh-spaces operator valued invariant kernels | cataloged article.we hilbert loynes valued hermitian kernels semigroups representations linearizations kolmogorov decompositions reproducing kernel spaces. dilation kolmogorov reproducing kernel representations unifies dilation nagy stinesprings dilation theorems. springer basel | non_dup | [] |
5237039 | 10.1007/s00020-012-2014-4 | The paper is devoted to optimization of resonances for Krein strings with
total mass and statical moment constraints. The problem is to design for a
given $\alpha \in \R$ a string that has a resonance on the line $\alpha + \i
\R$ with a minimal possible modulus of the imaginary part. We find optimal
resonances and strings explicitly.Comment: 9 pages, these results were extracted in a slightly modified form
from the earlier e-print arXiv:1103.4117 [math.SP] following an advise of a
journal's refere | Optimization of quasi-normal eigenvalues for Krein-Nudelman strings | optimization of quasi-normal eigenvalues for krein-nudelman strings | devoted resonances krein strings statical moment constraints. alpha alpha modulus imaginary part. resonances strings pages print math.sp advise refere | non_dup | [] |
2256708 | 10.1007/s00020-012-2027-z | For real bounded functions \Phi and \Psi of compact support, we prove the
norm resolvent convergence, as \epsilon and \nu tend to 0, of a family of
one-dimensional Schroedinger operators on the line of the form S_{\epsilon,
\nu}=
-D^2+\alpha\epsilon^{-2}\Phi(\epsilon^{-1}x)+\beta\nu^{-1}\Psi(\nu^{-1}x),
provided the ratio \nu/\epsilon has a finite or infinity limit. The limit
operator S_0 depends on the shape of \Phi and \Psi as well as on the limit of
ratio \nu/\epsilon. If the potential \alpha\Phi possesses a zero-energy
resonance, then S_0 describes a non trivial point interaction at the origin.
Otherwise S_0 is the direct sum of the Dirichlet half-line Schroedinger
operators.Comment: 20 pages, minor correction | 1D Schr\"{o}dinger operators with short range interactions: two-scale
regularization of distributional potentials | 1d schr\"{o}dinger operators with short range interactions: two-scale regularization of distributional potentials | norm resolvent epsilon tend schroedinger epsilon alpha epsilon epsilon beta epsilon infinity limit. epsilon. alpha possesses describes trivial origin. dirichlet schroedinger pages minor | non_dup | [] |
13641577 | 10.1007/s00020-013-2054-4 | This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems for general variable-coefficient divergence-form second-order elliptic partial differential equations are reduced to some systems of localized boundary-domain singular integral equations. Equivalence of the integral equations systems to the original boundary value problems is proved. It is established that the corresponding localized boundary-domain integral operators belong to the Boutet de Monvel algebra of pseudo-differential operators. Applying the Vishik-Eskin theory based on the factorization method, the Fredholm properties and invertibility of the operators are proved in appropriate Sobolev spaces.This research was supported by the grant EP/H020497/1: "Mathematical Analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems" from the EPSRC, UK | Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients | localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic pdes with variable matrix coefficients | print article. official publised accessed links below. copyright springer baselemploying localized potentials laplace dirichlet neumann robin divergence elliptic localized singular equations. equivalence proved. localized belong boutet monvel pseudo operators. vishik eskin factorization fredholm invertibility proved sobolev spaces.this mathematical localized epsrc | non_dup | [] |
2253115 | 10.1007/s00020-013-2057-1 | Let B=A+K where A is a bounded selfadjoint operator and K is an element of
the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an
enumeration of the discrete spectrum of B. We show that $\sum_n
\dist(\lambda_n, \sigma(A))^p$ is bounded from above by a constant multiple of
|K|_p^p. We also derive a unitary analog of this estimate and apply it to
obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section
5, additional references. To appear in Int. Eq. Op. Theor | Variation of discrete spectra for non-selfadjoint perturbations of
selfadjoint operators | variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators | selfadjoint neumann schatten ideal lambda enumeration dist lambda sigma derive unitary analog cauchy references. int. theor | non_dup | [] |
158832830 | 10.1007/s00020-013-2063-3 | Given a complex Krein space H with fundamental symmetry J, the aim of this note is to characterize the set of J-normal projections
Q={Q∈L(H):Q2=QandQ#Q=QQ#}.
The ranges of the projections in QQ are exactly those subspaces of HH which are pseudo-regular. For a fixed pseudo-regular subspace S , there are infinitely many J-normal projections onto it, unless SS is regular. Therefore, most of the material herein is devoted to parametrizing the set of J-normal projections onto a fixed pseudo-regular subspace S.Fil: Maestripieri, Alejandra Laura. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaFil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentin | Normal projections in Krein spaces | normal projections in krein spaces | krein characterize projections qandq ranges projections subspaces pseudo regular. pseudo subspace infinitely projections unless regular. herein devoted parametrizing projections pseudo subspace s.fil maestripieri alejandra laura. universidad buenos aires. facultad ingeniería argentina. consejo nacional investigaciones científicas técnicas. oficina coordinación administrativa saavedra instituto argentino matemática argentinafil martinez peria francisco dardo. consejo nacional investigaciones científicas técnicas. oficina coordinación administrativa saavedra instituto argentino matemática argentina. universidad nacional plata. facultad ciencias exactas argentin | non_dup | [] |
12828809 | 10.1007/s00020-013-2072-2 | The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied | Spectral estimates for resolvent differences of self-adjoint elliptic operators | spectral estimates for resolvent differences of self-adjoint elliptic operators | quasi triples weyl hilbert resolvent adjoint extensions ideals proved. adjoint realizations elliptic exterior potentials hypersurfaces | non_dup | [] |
24938202 | 10.1007/s00020-013-2093-x | We consider a regular indefinite Sturm-Liouville eigenvalue problem \{$-f" +
q f = \lambda r f$} on $[a,b]$ subject to general self-adjoint boundary
conditions and with a weight function $r$ which changes its sign at finitely
many, so-called turning points. We give sufficient and in some cases necessary
and sufficient conditions for the Riesz basis property of this eigenvalue
problem. In the case of separated boundary conditions we extend the class of
weight functions $r$ for which the Riesz basis property can be completely
characterized in terms of the local behavior of $r$ in a neighborhood of the
turning points. We identify a class of non-separated boundary conditions for
which, in addition to the local behavior of $r$ in a neighborhood of the
turning points, local conditions on $r$ near the boundary are needed for the
Riesz basis property. As an application, it is shown that the Riesz basis
property for the periodic boundary conditions is closely related to a regular
HELP-type inequality without boundary conditions.Comment: Integr. Equat. Oper. Theory (2013), to appea | The Riesz basis property of an indefinite Sturm-Liouville problem with
non-separated boundary conditions | the riesz basis property of an indefinite sturm-liouville problem with non-separated boundary conditions | indefinite sturm liouville eigenvalue lambda adjoint finitely turning points. riesz eigenvalue problem. separated extend riesz neighborhood turning points. separated neighborhood turning riesz property. riesz closely inequality integr. equat. oper. appea | non_dup | [] |
53288996 | 10.1007/s00020-013-2097-6 | Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T+K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of $T+K, such that f is non constant on each of the components of its domain | A unifying approach to Weyl type theorems for Banach space operators | a unifying approach to weyl type theorems for banach space operators | weyl theorems proved considerably operators. introducing quasi totally hereditarily normaloid weyl theorems promptly operators. entails weyl theorems perturbations algebraic commutes analytic neighborhood | non_dup | [] |
43553457 | 10.1007/s00020-014-2124-2 | Let $\mu$ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures $\mu$ such that the general family of spaces of analytic functions, $F (p,q,s)$ which contain many classical function spaces, including the Bloch space, $BMOA$ and the $Q_s$ spaces, are embedded boundedly or compactly into the tent-type spaces $T_{p,s}^\infty(\mu)$. The results are applied to characterize boundedness and compactness of Riemann-Stieltjes operators and multiplication operators on $F (p,q,s)$ | Carleson Measures, Riemann-Stieltjes and Multiplication Operators on a General Family of Function Spaces | carleson measures, riemann-stieltjes and multiplication operators on a general family of function spaces | nonnegative borel plane. characterize analytic bloch bmoa embedded boundedly compactly tent infty characterize boundedness compactness riemann stieltjes multiplication | non_dup | [] |
24954993 | 10.1007/s00020-014-2136-y | In earlier papers the second author and Charles Read have introduced and
studied a new notion of positivity for operator algebras, with an eye to
extending certain C*-algebraic results and theories to more general algebras.
The present paper consists of complements to some facts in the just mentioned
papers, concerning this notion of positivity. For example we prove a result on
the numerical range of products of the roots of commuting operators with
numerical range in a sector.Comment: 11 pages, to appear Integral Equations Operator Theor | On positivity and roots in operator algebras | on positivity and roots in operator algebras | papers charles read notion positivity algebras extending algebraic algebras. complements facts papers concerning notion positivity. roots commuting pages theor | non_dup | [] |
55632469 | 10.1007/s00020-014-2140-2 | We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a
mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.Fundação para a Ciência e a Tecnologia (FCT/Portugal), through Project PTDC/MAT/121837/2010 and Project Est- C/MAT/UI0013/2011. The first author was also supported by the Center for Mathematical
Analysis, Geometry, and Dynamical Systems and the second author was also supported by the Centre of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPET | Riemann–Hilbert problems, Toeplitz operators and Q-classes | riemann–hilbert problems, toeplitz operators and q-classes | generalize notion wiener–hopf factorization algebraic representations intersections explore connection equations. factorization toeplitz symbol class. theoretic results.fundação para ciência tecnologia portugal ptdc mathematical mathematics minho feder funds programa operacional factores competitividade compet | non_dup | [] |
52440221 | 10.1007/s00020-014-2143-z | For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of subspaces M\subset H such that M\capR=M^\perp\capR=\{0\}. We show how the existence of such subspaces leads to various {pathological} properties of {unbounded} self-adjoint operators related to von Neumann theorems \cite{Neumann}--\cite{Neumann2}. We revise the von Neumann-Van Daele-Schm\"udgen assertions \cite{Neumann}, \cite{Daele}, \cite{schmud} to refine them. We also develop {a new systematic approach, which allows to construct for any {unbounded} densely defined symmetric/self-adjoint operator T infinitely many pairs of its closed densely defined restrictions T_k\subset T such that \dom(T^* T_{k})=\{0\} (\Rightarrow \dom T_{k}^2=\{0\}$) k=1,2 and \dom T_1\cap\dom T_2=\{0\}, \dom T_1\dot+\dom T_2=\dom T | Around the Van Daele–Schmüdgen Theorem | around the van daele–schmüdgen theorem | adjoint acting infinite separable hilbert possessing dense propose characterisation phenomenon concerning subspaces capr perp capr subspaces pathological unbounded adjoint neumann theorems cite neumann cite neumann revise neumann daele schm udgen assertions cite neumann cite daele cite schmud refine them. unbounded densely adjoint infinitely densely restrictions rightarrow | non_dup | [] |
24943526 | 10.1007/s00020-014-2148-7 | Regular normalized W-valued spectral measures on a compact Hausdorff space X
are in one-to-one correspondence with unital *-representations \rho:C(X)\to W,
where W stands for a von Neumann algebra. In this paper we show that for every
compact Hausdorff space X and every von Neumann algebras W_1,W_2 there is a
one-to-one correspondence between unital *-representations \rho:C(X,W_1)\to W_2
and special B(W_1,W_2)-valued measures on X that we call non-negative spectral
measures. Such measures are special cases of non-negative measures that we
introduced in our previous paper in connection with moment problems for
operator polynomials.Comment: 20 page | Non-negative spectral measures and representations of C*-algebras | non-negative spectral measures and representations of c*-algebras | valued hausdorff correspondence unital representations stands neumann algebra. hausdorff neumann algebras correspondence unital representations valued call measures. connection moment | non_dup | [] |
24796035 | 10.1007/s00020-014-2166-5 | We consider Exel's interaction $(V,H)$ over a unital $C^*$-algebra $A$, such
that $V(A)$ and $H(A)$ are hereditary subalgebras of $A$. For the associated
crossed product, we obtain a uniqueness theorem, ideal lattice description,
simplicity criterion and a version of Pimsner-Voiculescu exact sequence. These
results cover the case of crossed products by endomorphisms with hereditary
ranges and complementary kernels. As model examples of interactions not coming
from endomorphisms we introduce and study in detail interactions arising from
finite graphs.
The interaction $(V,H)$ associated to a graph $E$ acts on the core $F_E$ of
the graph algebra $C^*(E)$. By describing a partial homeomorphism of
$\widehat{F}_E$ dual to $(V,H)$ we find Cuntz-Krieger uniqueness theorem,
criteria for gauge-invariance of all ideals and simplicity of $C^*(E)$ as
results concerning reversible noncommutative dynamics. We also provide a new
approach to calculation of $K$-theory of $C^*(E)$ using only an induced partial
automorphism of $K_0(F_E)$ and the six-term exact sequence.Comment: The term complete interaction changed to corner interaction. This
version is accepted to Integral Equations and Operator Theor | Crossed products for interactions and graph algebras | crossed products for interactions and graph algebras | exel unital hereditary subalgebras crossed uniqueness ideal simplicity criterion pimsner voiculescu sequence. cover crossed endomorphisms hereditary ranges complementary kernels. coming endomorphisms arising graphs. acts describing homeomorphism widehat cuntz krieger uniqueness invariance ideals simplicity concerning reversible noncommutative dynamics. automorphism changed corner interaction. theor | non_dup | [] |
25050820 | 10.1007/s00020-014-2178-1 | We establish the convergence of pseudospectra in Hausdorff distance for
closed operators acting in different Hilbert spaces and converging in the
generalised norm resolvent sense. As an assumption, we exclude the case that
the limiting operator has constant resolvent norm on an open set. We extend the
class of operators for which it is known that the latter cannot happen by
showing that if the resolvent norm is constant on an open set, then this
constant is the global minimum. We present a number of examples exhibiting
various resolvent norm behaviours and illustrating the applicability of this
characterisation compared to known results.Comment: 16 pages, 1 figur | Remarks on the convergence of pseudospectra | remarks on the convergence of pseudospectra | establish pseudospectra hausdorff acting hilbert converging generalised norm resolvent sense. exclude limiting resolvent norm set. extend happen resolvent norm minimum. exhibiting resolvent norm behaviours illustrating applicability characterisation pages figur | non_dup | [] |
24948465 | 10.1007/s00020-014-2193-2. | We give a characterization of the contraction ratio of bounded linear maps in
Banach space with respect to Hopf's oscillation seminorm, which is the
infinitesimal distance associated to Hilbert's projective metric, in terms of
the extreme points of a certain abstract "simplex". The formula is then applied
to abstract Markov operators defined on arbitrary cones, which extend the row
stochastic matrices acting on the standard positive cone and the completely
positive unital maps acting on the cone of positive semidefinite matrices. When
applying our characterization to a stochastic matrix, we recover the formula of
Dobrushin's ergodicity coefficient. When applying our result to a completely
positive unital map, we therefore obtain a noncommutative version of
Dobrushin's ergodicity coefficient, which gives the contraction ratio of the
map (representing a quantum channel or a "noncommutative Markov chain") with
respect to the diameter of the spectrum. The contraction ratio of the dual
operator (Kraus map) with respect to the total variation distance will be shown
to be given by the same coefficient. We derive from the noncommutative
Dobrushin's ergodicity coefficient an algebraic characterization of the
convergence of a noncommutative consensus system or equivalently the ergodicity
of a noncommutative Markov chain.Comment: An announcement of some of the present results has appeared in the
Proceedings of the ECC 2013 conference (Zurich). Further results can be found
in the companion arXiv:1302.522 | Dobrushin's ergodicity coefficient for Markov operators on cones | dobrushin's ergodicity coefficient for markov operators on cones | contraction banach hopf oscillation seminorm infinitesimal hilbert projective extreme simplex markov cones extend stochastic acting cone unital acting cone semidefinite matrices. stochastic recover dobrushin ergodicity coefficient. unital noncommutative dobrushin ergodicity contraction representing noncommutative markov spectrum. contraction kraus coefficient. derive noncommutative dobrushin ergodicity algebraic noncommutative consensus equivalently ergodicity noncommutative markov announcement appeared zurich companion | non_dup | [] |
25041709 | 10.1007/s00020-014-2198-x | We introduce a family of domains --- which we call the $\mu_{1,n}$-quotients
--- associated with an aspect of $\mu$-synthesis. We show that the natural
association that the symmetrized polydisc has with the corresponding spectral
unit ball is also exhibited by the $\mu_{1,n}$-quotient and its associated unit
"$\mu_E$-ball". Here, $\mu_E$ is the structured singular value for the case $E
= \{[w]\oplus(z I_{n-1})\in \mathbb{C}^{n\times n}: z,w\in \mathbb{C}\}$, n =
2, 3, 4,... Specifically: we show that, for such an $E$, the Nevanlinna-Pick
interpolation problem with matricial data in a unit "$\mu_E$-ball", and in
general position in a precise sense, is equivalent to a Nevanlinna-Pick
interpolation problem for the associated $\mu_{1,n}$-quotient. Along the way,
we present some characterizations for the $\mu_{1,n}$-quotients.Comment: 15 pages; added Remark 3.6 and an additional reference; to appear in
Integral Eqns. Operator Theor | A family of domains associated with $\mu$-synthesis | a family of domains associated with $\mu$-synthesis | call quotients aspect synthesis. symmetrized polydisc ball exhibited quotient ball structured singular oplus mathbb mathbb nevanlinna pick interpolation matricial ball precise nevanlinna pick interpolation quotient. characterizations pages remark eqns. theor | non_dup | [] |
29511001 | 10.1007/s00020-014-2206-1 | Let $\mathcal{M}$ be a semifinite von Neumann algebra with a faithful,
normal, semifinite trace $\tau$ and $E$ be a strongly symmetric Banach function
space on $[0,\tau(1))$. We show that an operator $x$ in the unit sphere of
$E\left(\mathcal{M},\tau\right)$ is $k$-extreme, $k\in\mathbb N$, whenever its
singular value function $\mu(x)$ is $k$-extreme and one of the following
conditions hold (i) $\mu(\infty,x)=\lim_{t\to\infty}\mu(t,x)=0$ or (ii)
$n(x)\mathcal{M} n(x^*)=0$ and $|x|\geq \mu(\infty,x)s(x)$, where $n(x)$ and
$s(x)$ are null and support projections of $x$, respectively. The converse is
true whenever $\mathcal{M}$ is non-atomic. The global $k$-rotundity property
follows, that is if $\mathcal{M}$ is non-atomic then $E$ is $k$-rotund if and
only if $E\left(\mathcal{M},\tau\right)$ is $k$-rotund. As a consequence of the
noncommutive results we obtain that $f$ is a $k$-extreme point of the unit ball
of the strongly symmetric function space $E$ if and only if its decreasing
rearrangement $\mu(f)$ is $k$-extreme and $|f|\geq \mu(\infty,f)$. We conclude
with the corollary on orbits $\Omega(g)$ and $\Omega'(g)$. We get that $f$ is a
$k$-extreme point of the orbit $\Omega(g)$, $g\in L_1+L_{\infty}$, or
$\Omega'(g)$, $g\in L_1[0,\alpha)$, $\alpha<\infty$, if and only if
$\mu(f)=\mu(g)$ and $|f|\geq \mu(\infty,f)$. From this we obtain a
characterization of $k$-extreme points in Marcinkiewicz spaces.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s00020-014-2206- | k-Extreme Points in Symmetric Spaces of Measurable Operators | k-extreme points in symmetric spaces of measurable operators | mathcal semifinite neumann faithful semifinite trace banach sphere mathcal extreme mathbb whenever singular extreme hold infty infty mathcal infty projections respectively. converse whenever mathcal atomic. rotundity mathcal rotund mathcal rotund. noncommutive extreme ball decreasing rearrangement extreme infty corollary orbits omega omega extreme orbit omega infty omega alpha alpha infty infty extreme marcinkiewicz publication springer | non_dup | [] |
25015535 | 10.1007/s00020-015-2221-x | Let $h_g^\infty$ be the space of harmonic functions in the unit ball that are
bounded by some increasing radial function $g(r)$ with $\lim_{r\rightarrow 1}
g(r)=+\infty$; these spaces are called growth spaces. We describe functions in
growth spaces by the Ces\`aro means of their expansions in harmonic polynomials
and apply this characterization to study coefficient multipliers between growth
spaces. A series of examples of multipliers is given and some results by A. L.
Shields and D. L. Williams and G. Bennett, D. A. Stegenga and R. M. Timoney are
generalized to harmonic functions in higher dimensions.Comment: Theorem 3 is added, small corrections are mad | Coefficient multipliers of growth spaces of harmonic functions | coefficient multipliers of growth spaces of harmonic functions | infty harmonic ball rightarrow infty spaces. expansions harmonic polynomials multipliers spaces. multipliers shields williams bennett stegenga timoney harmonic | non_dup | [] |
47083960 | 10.1007/s00020-015-2242-5 | International audienceIn [X. Claeys and R. Hiptmair, Integral equations on multi-screens. Integral Equ Oper Theory, 77(2):167–197, 2013] we developed a framework for the analysis of boundary integral equations for acoustic scattering at so-called multi-screens, which are arbitrary arrangements of thin panels made of impenetrable material. In this article we extend these considerations to boundary integral equations for electromagnetic scattering. We view tangential multi-traces of vector fields from the perspective of quotient spaces and introduce the notion of single-traces and spaces of jumps. We also derive representation formulas and establish key properties of the involved potentials and related boundary operators. Their coercivity will be proved using a splitting of jump fields. Another new aspect emerges in the form of surface differential operators linking various trace spaces | Integral Equations for Electromagnetic Scattering at Multi-Screens | integral equations for electromagnetic scattering at multi-screens | audiencein claeys hiptmair screens. oper acoustic screens arrangements panels impenetrable material. extend considerations electromagnetic scattering. tangential traces perspective quotient notion traces jumps. derive formulas establish potentials operators. coercivity proved splitting jump fields. aspect emerges linking trace | non_dup | [] |
29527767 | 10.1007/s00020-015-2248-z | A long series of previous papers have been devoted to the (one-dimensional)
moment problem with nonnegative rational measure. The rationality assumption is
a complexity constraint motivated by applications where a parameterization of
the solution set in terms of a bounded finite number of parameters is required.
In this paper we provide a complete solution of the multidimensional moment
problem with a complexity constraint also allowing for solutions that require a
singular measure added to the rational, absolutely continuous one. Such
solutions occur on the boundary of a certain convex cone of solutions. In this
paper we provide complete parameterizations of all such solutions. We also
provide errata for a previous paper in this journal coauthored by one of the
authors of the present paper.Comment: 25 pages. Revision: minor correction | The Multidimensional Moment Problem with Complexity Constraint | the multidimensional moment problem with complexity constraint | papers devoted moment nonnegative rational measure. rationality motivated parameterization required. multidimensional moment allowing singular rational absolutely one. convex cone solutions. parameterizations solutions. errata coauthored pages. revision minor | non_dup | [] |
38147916 | 10.1007/s00020-015-2251-4 | It is well-known that the state space isomorphism theorem fails in infinite-dimensional Hilbert spaces: there exist minimal discrete-time systems (with Hilbert space state spaces) which have the same impulse response, but which are not isomorphic. We consider discrete-time systems on locally convex topological vector spaces which are Hausdorff and barrelled and show that in this setting the state space isomorphism theorem does hold. In contrast to earlier work on topological vector spaces, we consider a definition of minimality based on dilations and show how this necessitates certain definitions of controllability and observability | The state space isomorphism theorem for discrete-time infinite-dimensional systems | the state space isomorphism theorem for discrete-time infinite-dimensional systems | isomorphism fails infinite hilbert hilbert impulse isomorphic. locally convex topological hausdorff barrelled isomorphism hold. topological minimality dilations necessitates definitions controllability observability | non_dup | [] |
24936848 | 10.1007/s00020-015-2253-2 | We establish several new relations between the discrete transition operator,
the continuous Laplacian and the averaging operator associated with
combinatorial and metric graphs. It is shown that these operators can be
expressed through each other using explicit expressions. In particular, we show
that the averaging operator is closely related with the solutions of the
associated wave equation. The machinery used allows one to study a class of
infinite graphs without assumption on the local finiteness.Comment: 32 page | New relations between discrete and continuous transition operators on
(metric) graphs | new relations between discrete and continuous transition operators on (metric) graphs | establish laplacian averaging combinatorial graphs. expressions. averaging closely equation. machinery infinite | non_dup | [] |
29545066 | 10.1007/s00020-015-2254-1 | In this article we develop a new abstract strategy for proving ergodicity
with explicit computable rate of convergence for diffusions associated with a
degenerate Kolmogorov operator L. A crucial point is that the evolution
operator L may have singular and nonsmooth coefficients. This allows the
application of the method e.g. to degenerate and singular particle systems
arising in Mathematical Physics. As far as we know in such singular cases the
relaxation to equilibrium can't be discussed with the help of existing
approaches using hypoellipticity, hypocoercivity or stochastic Lyapunov type
techniques. The method is formulated in an L2-Hilbert space setting and is
based on an interplay between Functional Analysis and Stochastics. Moreover, it
implies an ergodicity rate which can be related to L2-exponential convergence
of the semigroup. Furthermore, the ergodicity method shows up an interesting
analogy with existing hypocoercivity approaches. In the first application we
discuss ergodicity of the N-particle degenerate Langevin dynamics with singular
potentials. The dual to this equation is also called the kinetic Fokker-Planck
equation with an external confining potential. In the second example we apply
the method to the so-called (degenerate) spherical velocity Langevin equation
which is also known as the fiber lay-down process arising in industrial
mathematics.Comment: Older preprint version of the paper (from 2014). The final
publication is available at Springer via
http://dx.doi.org/10.1007/s00020-015-2254-1 It was published under the name
"A hypocoercivity related ergodicity method for singularly distorted
non-symmetric diffusions"; see Integral Equations Oper. Theory 83, No. 3,
Article ID 2254, 331-379 (2015 | A hypocoercivity related ergodicity method with rate of convergence for
singularly distorted degenerate Kolmogorov equations and applications | a hypocoercivity related ergodicity method with rate of convergence for singularly distorted degenerate kolmogorov equations and applications | proving ergodicity computable diffusions degenerate kolmogorov crucial singular nonsmooth coefficients. e.g. degenerate singular arising mathematical physics. singular relaxation hypoellipticity hypocoercivity stochastic lyapunov techniques. formulated hilbert interplay stochastics. ergodicity exponential semigroup. ergodicity analogy hypocoercivity approaches. ergodicity degenerate langevin singular potentials. fokker planck confining potential. degenerate spherical langevin fiber arising industrial older preprint publication springer name hypocoercivity ergodicity singularly distorted diffusions oper. | non_dup | [] |
25016730 | 10.1007/s00020-015-2264-z | A subnormal weighted shift may be transformed to another shift in various
ways, such as taking the p-th power of each weight or forming the Aluthge
transform. \ We determine in a number of cases whether the resulting shift is
subnormal, and, if it is, find a concrete representation of the associated
Berger measure, directly for finitely atomic measures, and using both Laplace
transform and Fourier transform methods for more complicated measures. \
Alternatively, the problem may be viewed in purely measure-theoretic terms as
the attempt to solve moment matching equations such as $(\int t^n \, d\mu(t))^2
= \int t^n \, d\nu(t)$ ($n=0, 1, \ldots$) for one measure given the other | Berger measure for some transformations of subnormal weighted shifts | berger measure for some transformations of subnormal weighted shifts | subnormal weighted transformed ways forming aluthge transform. subnormal concrete berger finitely laplace transform fourier transform complicated measures. alternatively viewed purely theoretic attempt solve moment matching ldots | non_dup | [] |
29518472 | 10.1007/s00020-016-2285-2 | The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff
\'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced
$C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique
extension is dense, and deduce that any representation of the reduced
$C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there
is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if
and only if the interior of the isotropy in $G$ is closed. Using this, we prove
that when the interior of the isotropy is abelian and closed, $M$ is a Cartan
subalgebra. We prove that for a large class of groupoids $G$ with abelian
isotropy---including all Deaconu--Renault groupoids associated to discrete
abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of
$k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by
example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for
pointing out the error); v2 shows there is a conditional expectation onto $M$
iff the interior of the isotropy is closed. v3: Material (including some
theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This
version published in Integral Equations and Operator Theor | Cartan subalgebras in C*-algebras of Hausdorff etale groupoids | cartan subalgebras in c*-algebras of hausdorff etale groupoids | interior isotropy hausdorff etale groupoid embeds subalgebra dense deduce injective faithful. conditional expectation interior isotropy closed. interior isotropy abelian cartan subalgebra. groupoids abelian isotropy deaconu renault groupoids abelian maximal abelian subalgebra. groupoids deduce maximal abelian pages. incorrect thanks kumjain pointing conditional expectation interior isotropy closed. statements rearranged shortened. removed. theor | non_dup | [] |
42639669 | 10.1007/s00020-016-2297-y | In this paper we discuss the problem of decomposition for unbounded $2\times
2$ operator matrices by a pair of complementary invariant graph subspaces.
Under mild additional assumptions, we show that such a pair of subspaces
decomposes the operator matrix if and only if its domain is invariant for the
angular operators associated with the graphs. As a byproduct of our
considerations, we suggest a new block diagonalization procedure that resolves
related domain issues. In the case when only a single invariant graph subspace
is available, we obtain block triangular representations for the operator
matrices.Comment: 21 pages. This paper provides a complete overhaul and extension to
the authors previous work arXiv:1307.6439 and includes an exampl | On invariant graph subspaces | on invariant graph subspaces | decomposition unbounded complementary subspaces. mild assumptions subspaces decomposes graphs. byproduct considerations diagonalization resolves issues. subspace triangular representations pages. overhaul exampl | non_dup | [] |
42672837 | 10.1007/s00020-016-2302-5 | The Wigner-von Neumann method, which was previously used for perturbing
continuous Schr\"{o}dinger operators, is here applied to their discrete
counterparts. In particular, we consider perturbations of arbitrary
$T$-periodic Jacobi matrices. The asymptotic behaviour of the subordinate
solutions is investigated, as too are their initial components, together giving
a general technique for embedding eigenvalues, $\lambda$, into the operator's
absolutely continuous spectrum. Introducing a new rational function,
$C(\lambda;T)$, related to the periodic Jacobi matrices, we describe the
elements of the a.c. spectrum for which this construction does not work (zeros
of $C(\lambda;T)$); in particular showing that there are only finitely many of
them | Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von
Neumann approach | eigenvalues for perturbed periodic jacobi matrices by the wigner-von neumann approach | wigner neumann perturbing schr dinger counterparts. perturbations jacobi matrices. asymptotic subordinate giving embedding eigenvalues lambda absolutely spectrum. introducing rational lambda jacobi a.c. zeros lambda finitely | non_dup | [] |
42662405 | 10.1007/s00020-016-2303-4 | We identify the norm of the semigroup generated by the non-self-adjoint
harmonic oscillator acting on $L^2(\Bbb{R})$, for all complex times where it is
bounded. We relate this problem to embeddings between Gaussian-weighted spaces
of holomorphic functions, and we show that the same technique applies, in any
dimension, to the semigroup $e^{-tQ}$ generated by an elliptic quadratic
operator acting on $L^2(\Bbb{R}^n)$. The method used --- identifying the
exponents of sharp products of Mehler formulas --- is elementary and is
inspired by more general works of L. H\"ormander, A. Melin, and J. Sj\"ostrand.Comment: 22 pages, 1 figure. Significant revision following referee's
comments. To appear in Integral Equations and Operator Theory; published
version may diffe | The norm of the non-self-adjoint harmonic oscillator semigroup | the norm of the non-self-adjoint harmonic oscillator semigroup | norm semigroup adjoint harmonic oscillator acting bounded. relate embeddings weighted holomorphic applies semigroup elliptic quadratic acting identifying exponents sharp mehler formulas elementary inspired ormander melin pages figure. revision referee comments. diffe | non_dup | [] |
73359044 | 10.1007/s00020-016-2311-4 | We study the spectrum of a self-adjoint Dirac-Krein operator with potential
on a compact star graph $\mathcal G$ with a finite number $n$ of edges. This
operator is defined by a Dirac-Krein differential expression with summable
matrix potentials on each edge, by self-adjoint boundary conditions at the
outer vertices, and by a self-adjoint matching condition at the common central
vertex of $\mathcal G$. Special attention is paid to Robin matching conditions
with parameter $\tau \in\mathbb R\cup\{\infty\}$. Choosing the decoupled
operator with Dirichlet condition at the central vertex as a reference
operator, we derive Krein's resolvent formula, introduce corresponding
Weyl-Titchmarsh functions, study the multiplicities, dependence on $\tau$, and
interlacing properties of the eigenvalues, and prove a trace formula. Moreover,
we show that, asymptotically for $R\to \infty$, the difference of the number of
eigenvalues in the intervals $[0,R)$ and $[-R,0)$ deviates from some integer
$\kappa_0$, which we call dislocation index, at most by $n+2$.Comment: Accepted for publication in IEO | Dirac-Krein systems on star graphs | dirac-krein systems on star graphs | adjoint dirac krein mathcal edges. dirac krein summable potentials adjoint outer adjoint matching mathcal paid robin matching mathbb infty choosing decoupled dirichlet derive krein resolvent weyl titchmarsh multiplicities interlacing eigenvalues trace formula. asymptotically infty eigenvalues intervals deviates integer kappa call dislocation .comment publication | non_dup | [] |
73366975 | 10.1007/s00020-016-2316-z | The Cesaro operator $\mathsf{C}$, when acting in the classical growth Banach
spaces $A^{-\gamma}$ and $A_0^{-\gamma}$, for $\gamma > 0 $, of analytic
functions on $\mathbb{D}$, is investigated. Based on a detailed knowledge of
their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the
norms of these operators precisely. It is then possible to characterize the
mean ergodic and related properties of $\mathsf{C}$ acting in these spaces. In
addition, we determine the largest Banach space of analytic functions on
$\mathbb{D}$ which $\mathsf{C}$ maps into $A^{-\gamma}$ (resp. into
$A_0^{-\gamma}$); this optimal domain space always contains $A^{-\gamma}$
(resp. $A_0^{-\gamma}$) as a proper subspace.Comment: 17 page | The Cesaro operator in growth Banach spaces of analytic functions | the cesaro operator in growth banach spaces of analytic functions | cesaro mathsf acting banach gamma gamma gamma analytic mathbb investigated. aleman persson norms precisely. characterize ergodic mathsf acting spaces. banach analytic mathbb mathsf gamma resp. gamma gamma resp. gamma proper | non_dup | [] |
42643031 | 10.1007/s00020-016-2320-3 | Let $\mathscr{H}^2$ denote the space of ordinary Dirichlet series with square
summable coefficients, and let $\mathscr{H}^2_0$ denote its subspace consisting
of series vanishing at $+\infty$. We investigate the weak product spaces
$\mathscr{H}^2\odot\mathscr{H}^2$ and $\mathscr{H}^2_0\odot\mathscr{H}^2_0$,
finding that several pertinent problems are more tractable for the latter
space. This surprising phenomenon is related to the fact that
$\mathscr{H}^2_0\odot\mathscr{H}^2_0$ does not contain the infinite-dimensional
subspace of $\mathscr{H}^2$ of series which lift to linear functions on the
infinite polydisc.
The problems considered stem from questions about the dual spaces of these
weak product spaces, and are therefore naturally phrased in terms of
multiplicative Hankel forms. We show that there are bounded, even Schatten
class, multiplicative Hankel forms on $\mathscr{H}^2_0 \times \mathscr{H}^2_0$
whose analytic symbols are not in $\mathscr{H}^2$. Based on this result we
examine Nehari's theorem for such Hankel forms. We define also the skew product
spaces associated with $\mathscr{H}^2\odot\mathscr{H}^2$ and
$\mathscr{H}^2_0\odot\mathscr{H}^2_0$, with respect to both half-plane and
polydisc differentiation, the latter arising from Bohr's point of view. In the
process we supply square function characterizations of the Hardy spaces
$\mathscr{H}^p$, for $0 < p < \infty$, from the viewpoints of both types of
differentiation. Finally we compare the skew product spaces to the weak product
spaces, leading naturally to an interesting Schur multiplier problem.Comment: This paper has been accepted for publication in Integral Equations
and Operator Theor | Weak product spaces of Dirichlet series | weak product spaces of dirichlet series | mathscr ordinary dirichlet summable mathscr subspace consisting vanishing infty mathscr odot mathscr mathscr odot mathscr pertinent tractable space. surprising phenomenon mathscr odot mathscr infinite subspace mathscr lift infinite polydisc. naturally phrased multiplicative hankel forms. schatten multiplicative hankel mathscr mathscr analytic symbols mathscr examine nehari hankel forms. skew mathscr odot mathscr mathscr odot mathscr polydisc arising bohr view. supply characterizations hardy mathscr infty viewpoints differentiation. skew naturally schur multiplier publication theor | non_dup | [] |
83837640 | 10.1007/s00020-017-2361-2 | We determine the boundedness and compactness of a large class of operators,
mapping from general Banach spaces of holomorphic functions into a particular
type of spaces of functions determined by the growth of the functions, or the
growth of the functions derivatives. The results show that the boundedness and
compactness of such intrinsic operators depends only on the behaviour on the
point evaluation functionals. They also generalize previous similar results
about several specific classes of operators, such as the multiplication,
composition and integral operators.Comment: 22 pages; the final publication is available at Springer via
http://dx.doi.org/10.1007/s00020-017-2361- | Intrinsic operators from holomorphic function spaces to growth spaces | intrinsic operators from holomorphic function spaces to growth spaces | boundedness compactness banach holomorphic derivatives. boundedness compactness intrinsic functionals. generalize multiplication pages publication springer | non_dup | [] |
73378874 | 10.1007/s00020-017-2365-y | Kadison's Pythagorean theorem (2002) provides a characterization of the
diagonals of projections with a subtle integrality condition. Arveson (2007),
Kaftal, Ng, Zhang (2009), and Argerami (2015) all provide different proofs of
that integrality condition. In this paper we interpret the integrality
condition in terms of the essential codimension of a pair of projections
introduced by Brown, Douglas and Fillmore (1973), or, equivalently of the index
of a Fredholm pair of projections introduced by Avron, Seiler, and Simon
(1994). The same techniques explain the integer occurring in the
characterization of diagonals of selfadjoint operators with finite spectrum by
Bownik and Jasper (2015).Comment: 15 page | Kadison's Pythagorean Theorem and essential codimension | kadison's pythagorean theorem and essential codimension | kadison pythagorean diagonals projections subtle integrality condition. arveson kaftal argerami proofs integrality condition. interpret integrality codimension projections brown douglas fillmore equivalently fredholm projections avron seiler simon integer occurring diagonals selfadjoint bownik jasper .comment | non_dup | [] |
29563597 | 10.1007/s00020-017-2368-8 | Quasi-normal-eigenvalue optimization is studied under constraints $b_1(x) \le
B(x) \le b_2 (x)$ on structure functions $B$ of 2-side open optical or
mechanical resonators. We prove existence of various optimizers and provide an
example when different structures generate the same optimal
quasi-(normal-)eigenvalue. To show that quasi-eigenvalues locally optimal in
various senses are in the spectrum $\Sigma^{nl}$ of the bang-bang eigenproblem
$y" = - \omega^2 y [ b_1 + (b_2 - b_1) \chi_{\mathbb{C}_+} (y^2 ) ]$, where
$\chi_{\mathbb{C}_+} (\cdot)$ is the indicator function of the upper complex
half-plane $\mathbb{C}_+$, we obtain a variational characterization of the
nonlinear spectrum $\Sigma^{nl}$ in terms of quasi-eigenvalue perturbations. To
address the minimization of the decay rate $| \mathrm{Im} \ \omega |$, we study
the bang-bang equation and explain how it excludes an unknown optimal $B$ from
the optimization process. Computing one of minimal decay structures for 1-side
open settings, we show that it resembles gradually size-modulated 1-D stack
cavities introduced recently in Optical Engineering. In 2-side open symmetric
settings, our example has an additional centered defect. Nonexistence of global
decay rate minimizers is discussed.Comment: 39 pages, 2 figures, 2 tables. The results of the paper were
partially reported at the International Congress of Mathematicians (Seoul ICM
2014) and in several seminar and workshop talk | Nonlinear bang-bang eigenproblems and optimization of resonances in
layered cavities | nonlinear bang-bang eigenproblems and optimization of resonances in layered cavities | quasi eigenvalue resonators. optimizers quasi eigenvalue. quasi eigenvalues locally senses sigma bang bang eigenproblem omega mathbb mathbb cdot indicator mathbb variational sigma quasi eigenvalue perturbations. minimization mathrm omega bang bang excludes unknown process. settings resembles gradually modulated stack cavities engineering. settings centered defect. nonexistence minimizers pages tables. partially congress mathematicians seoul seminar workshop talk | non_dup | [] |
83853887 | 10.1007/s00020-017-2370-1 | The purpose of the paper is to analyze frames $\{f_k\}_{k\in \mathbf Z}$
having the form $\{T^kf_0\}_{k\in\mathbf Z}$ for some linear operator $T:
\mbox{span} \{f_k\}_{k\in \mathbf Z} \to \mbox{span}\{f_k\}_{k\in \mathbf Z}$.
A key result characterizes boundedness of the operator $T$ in terms of
shift-invariance of a certain sequence space. One of the consequences is a
characterization of the case where the representation $\{f_k\}_{k\in \mathbf
Z}=\{T^kf_0\}_{k\in\mathbf Z}$ can be achieved for an operator $T$ that has an
extension to a bounded bijective operator $\widetilde{T}: \cal H \to \cal H.$
In this case we also characterize all the dual frames that are representable in
terms of iterations of an operator $V;$ in particular we prove that the only
possible operator is $V=(\widetilde{T}^*)^{-1}.$ Finally, we consider stability
of the representation $\{T^kf_0\}_{k\in\mathbf Z};$ rather surprisingly, it
turns out that the possibility to represent a frame on this form is sensitive
towards some of the classical perturbation conditions in frame theory. Various
ways of avoiding this problem will be discussed. Throughout the paper the
results will be connected with the operators and function systems appearing in
applied harmonic analysis, as well as with general group representations | Operator representations of frames: boundedness, duality, and stability | operator representations of frames: boundedness, duality, and stability | analyze frames mathbf mathbf mbox span mathbf mbox span mathbf characterizes boundedness invariance space. consequences mathbf mathbf bijective widetilde characterize frames representable iterations widetilde mathbf surprisingly turns perturbation theory. ways avoiding discussed. appearing harmonic representations | non_dup | [] |
83834001 | 10.1007/s00020-017-2377-7 | In contrast with the well-known methods of matching asymptotics and
multiscale (or compound) asymptotics, the " functional analytic approach " of
Lanza de Cristoforis (Analysis 28, 2008) allows to prove convergence of
expansions around interior small holes of size $\epsilon$ for solutions of
elliptic boundary value problems. Using the method of layer potentials, the
asymptotic behavior of the solution as $\epsilon$ tends to zero is described
not only by asymptotic series in powers of $\epsilon$, but by convergent power
series. Here we use this method to investigate the Dirichlet problem for the
Laplace operator where holes are collapsing at a polygonal corner of opening
$\omega$. Then in addition to the scale $\epsilon$ there appears the scale
$\eta = \epsilon^{\pi/\omega}$. We prove that when $\pi/\omega$ is irrational,
the solution of the Dirichlet problem is given by convergent series in powers
of these two small parameters. Due to interference of the two scales, this
convergence is obtained, in full generality, by grouping together integer
powers of the two scales that are very close to each other. Nevertheless, there
exists a dense subset of openings $\omega$ (characterized by Diophantine
approximation properties), for which real analyticity in the two variables
$\epsilon$ and $\eta$ holds and the power series converge unconditionally. When
$\pi/\omega$ is rational, the series are unconditionally convergent, but
contain terms in log $\epsilon$.Comment: Integral Equations and Operator Theory, Springer Verlag, 201 | Converging expansions for Lipschitz self-similar perforations of a plane
sector | converging expansions for lipschitz self-similar perforations of a plane sector | matching asymptotics multiscale compound asymptotics analytic lanza cristoforis expansions interior holes epsilon elliptic problems. potentials asymptotic epsilon tends asymptotic powers epsilon convergent series. dirichlet laplace holes collapsing polygonal corner opening omega epsilon epsilon omega omega irrational dirichlet convergent powers parameters. interference generality grouping integer powers other. nevertheless dense openings omega diophantine analyticity epsilon converge unconditionally. omega rational unconditionally convergent epsilon .comment springer verlag | non_dup | [] |
42704661 | 10.1007/s00020-017-2379-5. | We give an example of a scalar second order differential operator in the
plane with double periodic coefficients and describe its modification, which
causes an additional spectral band in the essential spectrum. The modified
operator is obtained by applying to the coefficients a mirror reflection with
respect to a vertical or horizontal line. This change gives rise to Rayleigh
type waves localized near the line. The results are proven using asymptotic
analysis, and they are based on high contrast of the coefficient functions.Comment: 14 pages, 3 figure | Effects of Rayleigh waves on the essential spectrum in perturbed doubly
periodic elliptic problems | effects of rayleigh waves on the essential spectrum in perturbed doubly periodic elliptic problems | modification spectrum. mirror reflection line. rayleigh localized line. proven asymptotic pages | non_dup | [] |
73953831 | 10.1007/s00020-017-2383-9 | The unitary correlation sets defined by the first author in conjunction with
tensor products of $\mathcal{U}_{nc}(n)$ are further studied. We show that
Connes' embedding problem is equivalent to deciding whether or not two smaller
versions of the unitary correlation sets are equal. Moreover, we obtain the
result that Connes' embedding problem is equivalent to deciding whether or not
two cross norms on $M_n \otimes M_n$ are equal for all $n \geq 2$.Comment: 24 pages, fixed a small error in the proof of Theorem 5.3 (v2 | Unitary Correlation Sets | unitary correlation sets | unitary conjunction mathcal studied. connes embedding deciding versions unitary equal. connes embedding deciding norms otimes .comment pages | non_dup | [] |
73351977 | 10.1007/s00020-017-2385-7 | We introduce GBDT version of Darboux transformation for symplectic and
Hamiltonian systems as well as for Shin-Zettl systems and Sturm-Liouville
equations. These are the first results on Darboux transformation for
general-type Hamiltonian and for Shin-Zettl systems. The obtained results are
applied to the corresponding transformations of the Weyl-Titchmarsh functions
and to the construction of explicit solutions of dynamical symplectic systems,
of two-way diffusion equations and of indefinite Sturm-Liouville equations. The
energy of the explicit solutions of dynamical systems is expressed (in a quite
simple form) in terms of the parameter matrices of GBDT.Comment: Section 7 of this paper is related to our recent paper
arXiv:1603.0870 | Hamiltonian systems and Sturm-Liouville equations: Darboux
transformation and applications | hamiltonian systems and sturm-liouville equations: darboux transformation and applications | gbdt darboux symplectic shin zettl sturm liouville equations. darboux shin zettl systems. transformations weyl titchmarsh symplectic indefinite sturm liouville equations. | non_dup | [] |
73420694 | 10.1007/s00020-017-2405-7 | In this paper we study the regularity of the Szeg\H{o} projection on Lebesgue
and Sobolev spaces on the distinguished boundary of the unbounded model worm
domain $D_\beta$.
We denote by $d_b(D_\beta)$ the distinguished boundary of $D_\beta$ and
define the corresponding Hardy space $\mathscr{H}^2(D_\beta)$. This can be
identified with a closed subspace of $L^2(d_b(D_\beta),d\sigma)$, that we
denote by $\mathscr{H}^2(d_b(D_\beta))$, where $d\sigma$ is the naturally
induced measure on $d_b(D_\beta)$.
The orthogonal Hilbert space projection $\mathscr{P}:
L^2(d_b(D_\beta),d\sigma)\to \mathscr{H}^2(d_b(D_\beta))$ is called the
Szeg\H{o} projection on the distinguished boundary.
We prove that $\mathscr{P}$, initially defined on the dense subspace
$L^2(d_b( D_\beta),d\sigma)\cap L^p(d_b(D_\beta), d\sigma)$ extends to a
bounded operator $\mathscr{P}: L^p(d_b(D_\beta), d\sigma)\to L^p(d_b(D_\beta),
d\sigma)$ if and only if
$\textstyle{\frac{2}{1+\nu_\beta}}<p<\textstyle{\frac{2}{1-\nu_\beta}}$ where
$\nu_\beta=\textstyle{\frac{\pi}{2\beta-\pi}},\beta>\pi$. Furthermore, we also
prove that $\mathscr{P}$ defines a bounded operator $\mathscr{P}:
W^{s,2}(d_b(D_\beta),d\sigma)\to W^{s,2}(d_b(D_\beta), d\sigma)$ if and only if
$0\leq s<\textstyle{\frac{\nu_\beta}{2}}$ where $W^{s.2}(d_b( D_\beta),
d\sigma)$ denotes the Sobolev space of order $s$ and underlying $L^2$-norm.
Finally, we prove a necessary condition for the boundedness of $\mathscr{P}$
on $W^{s,p}(d_b(D_\beta), d\sigma)$, $p\in(1,\infty)$, the Sobolev space of
order $s$ and underlying $L^p$-norm.Comment: 27 page | Sharp estimates for the Szeg\H{o} projection on the distinguished
boundary of model worm domains | sharp estimates for the szeg\h{o} projection on the distinguished boundary of model worm domains | regularity szeg projection lebesgue sobolev distinguished unbounded worm beta beta distinguished beta hardy mathscr beta subspace beta sigma mathscr beta sigma naturally beta orthogonal hilbert projection mathscr beta sigma mathscr beta szeg projection distinguished boundary. mathscr initially dense subspace beta sigma beta sigma extends mathscr beta sigma beta sigma textstyle frac beta textstyle frac beta beta textstyle frac beta beta mathscr defines mathscr beta sigma beta sigma textstyle frac beta beta sigma sobolev norm. boundedness mathscr beta sigma infty sobolev | non_dup | [] |
83869437 | 10.1007/s00020-017-2409-3 | If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let
$\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu _{n, k})_{n,k\ge
0}$ with entries $\mu _{n, k}=\mu _{n+k}$, where, for $n\,=\,0, 1, 2, \dots $,
$\mu_n$ denotes the moment of order $n$ of $\mu $. This matrix induces formally
the operator $$\mathcal{H}_\mu (f)(z)=
\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \mu_{n,k}{a_k}\right)z^n$$ on the
space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit
disc $\mathbb D $. This is a natural generalization of the classical Hilbert
operator. In this paper we improve the results obtained in some recent papers
concerning the action of the operators $H_\mu $ on Hardy spaces and on M\"obius
invariant spaces.Comment: arXiv admin note: text overlap with arXiv:1612.0830 | A Hankel matrix acting on spaces of analytic functions | a hankel matrix acting on spaces of analytic functions | borel mathcal hankel mathcal entries dots moment induces formally mathcal infty infty analytic infty disc mathbb generalization hilbert operator. papers concerning hardy obius admin overlap | non_dup | [] |
86415224 | 10.1007/s00020-018-2446-6 | We show that the classical Hamburger moment problem can be included in the
spectral theory of generalized indefinite strings. Namely, we introduce the
class of Krein-Langer strings and show that there is a bijective correspondence
between moment sequences and this class of generalized indefinite strings. This
result can be viewed as a complement to the classical results of M. G. Krein on
the connection between the Stieltjes moment problem and Krein-Stieltjes strings
and I. S. Kac on the connection between the Hamburger moment problem and 2x2
canonical systems with Hamburger Hamiltonians.Comment: 25 page | The Classical Moment Problem and Generalized Indefinite Strings | the classical moment problem and generalized indefinite strings | hamburger moment indefinite strings. krein langer strings bijective correspondence moment indefinite strings. viewed complement krein connection stieltjes moment krein stieltjes strings connection hamburger moment canonical hamburger | non_dup | [] |
29556678 | 10.1007/s00020-018-2453-7 | It is explained how a locally convex (lc) topology $\tau$ on a real vector
space $V$ extends to a locally multiplicatively convex (lmc) topology
$\overline{\tau}$ on the symmetric algebra $S(V)$. This allows the application
of the results on lmc topological algebras obtained by Ghasemi, Kuhlmann and
Marshall to obtain representations of $\overline{\tau}$-continuous linear
functionals $L: S(V)\rightarrow \mathbb{R}$ satisfying $L(\sum S(V)^{2d})
\subseteq [0,\infty)$ (more generally, $L(M) \subseteq [0,\infty)$ for some
$2d$-power module $M$ of $S(V)$) as integrals with respect to uniquely
determined Radon measures $\mu$ supported by special sorts of closed balls in
the dual space of $V$. The result is simultaneously more general and less
general than the corresponding result of Berezansky, Kondratiev and \v Sifrin.
It is more general because $V$ can be any lc topological space (not just a
separable nuclear space), the result holds for arbitrary $2d$-powers (not just
squares), and no assumptions of quasi-analyticity are required. It is less
general because it is necessary to assume that $L : S(V) \rightarrow
\mathbb{R}$ is $\overline{\tau}$-continuous (not just continuous on each
homogeneous part of $S(V)$).Comment: 19 pages, revised according to referee's comments, updated
references, to appear in Integral Equations and Operator Theor | Moment problem for symmetric algebras of locally convex spaces | moment problem for symmetric algebras of locally convex spaces | locally convex topology extends locally multiplicatively convex topology overline topological algebras ghasemi kuhlmann marshall representations overline functionals rightarrow mathbb satisfying subseteq infty subseteq infty module integrals uniquely radon sorts balls simultaneously berezansky kondratiev sifrin. topological separable powers squares assumptions quasi analyticity required. rightarrow mathbb overline homogeneous .comment pages revised referee comments updated theor | non_dup | [] |
83856794 | 10.1007/s00020-018-2461-7 | We consider Fredholm determinants of the form identity minus product of
spectral projections corresponding to isolated parts of the spectrum of a pair
of self-adjoint operators. We show an identity relating such determinants to an
integral over the spectral shift function in the case of a rank-one
perturbation. More precisely, we prove $$ -\ln \left(\det \big(\mathbf{1}
-\mathbf{1} _{I}(A) \mathbf{1}_{\mathbb R\backslash I}(B)\mathbf{1}_{I}(A)\big)
\right) = \int_I \text{d} x \int_{\mathbb R\backslash I} \text{d} y\,
\frac{\xi(x)\xi(y)}{(y-x)^2}, $$ where $\mathbf{1}_J (\cdot)$ denotes the
spectral projection of a self-adjoint operator on a set $J\in
\text{Borel}(\mathbb R)$. The operators $A$ and $B$ are self-adjoint, bounded
from below and differ by a rank-one perturbation and $\xi$ denotes the
corresponding spectral shift function. The set $I$ is a union of intervals on
the real line such that its boundary lies in the resolvent set of $A$ and $B$
and such that the spectral shift function vanishes there i.e. $I$ contains
isolated parts of the spectrum of $A$ and $B$. We apply this formula to the
subspace perturbation problem.Comment: version as publishe | On an integral formula for Fredholm determinants related to pairs of
spectral projections | on an integral formula for fredholm determinants related to pairs of spectral projections | fredholm determinants minus projections adjoint operators. relating determinants perturbation. precisely mathbf mathbf mathbf mathbb backslash mathbf mathbb backslash frac mathbf cdot projection adjoint borel mathbb adjoint perturbation function. union intervals lies resolvent vanishes i.e. subspace perturbation publishe | non_dup | [] |
83868489 | 10.1007/s00020-018-2475-1 | We introduce two natural notions of multivariable Aluthge transforms (toral
and spherical), and study their basic properties. In the case of 2-variable
weighted shifts, we first prove that the toral Aluthge transform does not
preserve (joint) hyponormality, in sharp contrast with the 1-variable case.
Second, we identify a large class of 2-variable weighted shifts for which
hyponormality is preserved under both transforms. Third, we consider whether
these Aluthge transforms are norm-continuous. Fourth, we study how the Taylor
and Taylor essential spectra of 2-variable weighted shifts behave under the
toral and spherical Aluthge transforms; as a special case, we consider the
Aluthge transforms of the Drury-Arveson 2-shift. Finally, we briefly discuss
the class of spherically quasinormal 2-variable weighted shifts, which are the
fixed points for the spherical Aluthge transform | Aluthge transforms of 2-variable weighted shifts | aluthge transforms of 2-variable weighted shifts | notions multivariable aluthge transforms toral spherical properties. weighted shifts toral aluthge transform preserve hyponormality sharp case. weighted shifts hyponormality preserved transforms. aluthge transforms norm continuous. fourth taylor taylor weighted shifts behave toral spherical aluthge transforms aluthge transforms drury arveson shift. briefly spherically quasinormal weighted shifts spherical aluthge transform | non_dup | [] |
141530921 | 10.1007/s00020-018-2486-y | We investigate the spectrum of the three-dimensional Dirichlet Laplacian in a
prototypal infinite polyhedral layer, that is formed by three perpendicular
quarter-plane walls of constant width joining each other. Alternatively, this
domain can be viewed as an octant from which another "parallel" octant is
removed. It contains six edges (three convex and three non-convex) and two
corners (one convex and one non-convex). It is a canonical example of
non-smooth conical layer. We name it after Fichera because near its non-convex
corner, it coincides with the famous Fichera cube that illustrates the
interaction between edge and corner singularities. This domain could also be
called an octant layer.
We show that the essential spectrum of the Laplacian on such a domain is a
half-line and we characterize its minimum as the first eigenvalue of the
two-dimensional Laplacian on a broken guide. By a Born-Oppenheimer type
strategy, we also prove that its discrete spectrum is finite and that a lower
bound is given by the ground state of a special Sturm-Liouville operator. By
finite element computations taking singularities into account, we exhibit
exactly one eigenvalue under the essential spectrum threshold leaving a
relative gap of 3%. We extend these results to a variant of the Fichera layer
with rounded edges (for which we find a very small relative gap of 0.5%), and
to a three-dimensional cross where the three walls are full thickened planes.Comment: 33 page | Dirichlet spectrum of the Fichera layer | dirichlet spectrum of the fichera layer | dirichlet laplacian prototypal infinite polyhedral perpendicular quarter walls joining other. alternatively viewed octant octant removed. convex convex corners convex convex canonical conical layer. name fichera convex corner coincides famous fichera cube illustrates corner singularities. octant layer. laplacian characterize eigenvalue laplacian broken guide. born oppenheimer sturm liouville operator. computations singularities exhibit eigenvalue leaving extend variant fichera rounded walls thickened | non_dup | [] |
52774537 | 10.1007/s00021-004-0128-4 | International audienceThe standing gravity wave problem on an infinitely deep fluid layer is considered under the form of a nonlinear non local scalar PDE of second order as in [6]. Nonreso-nance at quadratic order of the infinite dimensional bifurcation equation, allows to give the explicit form of the quadratic change of variables able to suppress quadratic terms in the nonlinear equation. We state precisely the equivalence between formulations in showing that the above unbounded change of variable is invertible. The infinite set of solutions which can be expanded in powers of amplitude ε is then given up to order ε 2 | Multimodal Standing Gravity Waves: a Completely Resonant System | multimodal standing gravity waves: a completely resonant system | audiencethe standing infinitely nonreso nance quadratic infinite bifurcation quadratic suppress quadratic equation. precisely equivalence formulations unbounded invertible. infinite expanded powers | non_dup | [] |
52793697 | 10.1007/s00021-004-0145-3 | International audienceWe consider bifurcations of a class of infinite dimensional reversible dynamical systems which possess a family of symmetric equilibria near the origin. We also assume that the linearized operator at the origin $% L_{\varepsilon }$ has an essential spectrum filling the entire real line, in addition to the simple eigenvalue at 0. Moreover, for parameter values $% \varepsilon <0$ there is a pair of imaginary eigenvalues which meet in 0 for $\varepsilon =0$, and which disappear for $\varepsilon >0$. The above situation occurs for example when one looks for travelling waves in a system of superposed perfect fluid layers, one being infinitely deep. We give quite general assumptions which apply in such physical examples, under which one obtains a family of bifurcating solutions homoclinic to every equilibrium near the origin. These homoclinics are symmetric and decay algebraically at infinity, being approximated at main order by the Benjamin - Ono homoclinic. For the water wave example, this corresponds to a family of solitary waves, such that at infinity the upper layer slides with a uniform velocity, over the bottom layer (at rest) | Reversible Bifurcation of Homoclinic Solutions in Presence of an Essential Spectrum | reversible bifurcation of homoclinic solutions in presence of an essential spectrum | audiencewe bifurcations infinite reversible possess equilibria origin. linearized varepsilon filling eigenvalue varepsilon imaginary eigenvalues meet varepsilon disappear varepsilon looks travelling superposed perfect infinitely deep. assumptions obtains bifurcating homoclinic origin. homoclinics algebraically infinity approximated benjamin homoclinic. solitary infinity slides | non_dup | [] |
52774536 | 10.1007/s00021-005-0164-8 | International audienceWe consider two-dimensional standing gravity waves on the surface of an infinitely deep perfect fluid, the flow being potential. It is known that the linearized problem is completely resonant. Following the method described in [4], we prove the existence of an infinity of multimodal standing gravity waves, corresponding to any choice of asymptotic expansion in powers of the amplitude ε, indicated in [2] and [3]. Each one of these solutions exist for a set of values of ε being dense in 0 | Existence of Multimodal Standing Gravity Waves | existence of multimodal standing gravity waves | audiencewe standing infinitely perfect potential. linearized resonant. infinity multimodal standing asymptotic powers dense | non_dup | [] |
53979439 | 10.1007/s00021-006-6113-z | Objective and design: We investigated the antinociceptiveeffect of paracetamol or morphine after repeatedadministration and the changes in the characteristics of centralμ-, κ- and 5-HT2 receptors.Treatment: Male rats were injected twice a day for sevendays with paracetamol (400 mg/kg, i. p.) or morphine (5 mg/kg, s. c.).Methods: The antinociceptive effect was evaluated 30 minafter single and multiple doses of paracetamol and morphinethrough the hot-plate test. Binding techniques were used toevaluate the receptor characteristics in the frontal cortex.Results: Both paracetamol and morphine induced an antinociceptiveeffect on day 1 but only paracetamol maintainedthis effect for seven days while morphine did not.The number of μ-opioid receptors decreased on days 1, 3,and 7 by a similar percentage after paracetamol administration(by 29, 31 and 34 %, respectively), while morphineproduced a progressive decrease in comparison with controls(by 37, 49 and 60 %, respectively) and κ-opioid receptorswere unaffected. Both drugs similarly decreased the 5-HT2receptor number on all days of treatment (by about 30 %).Conclusions: The opioidergic and serotonergic systems areinvolved in different ways in the induction and maintenanceof antinociception after paracetamol or morphine treatment | Effect of acute and repeated administration of paracetamol on opioidergic and serotonergic systems in rats. | effect of acute and repeated administration of paracetamol on opioidergic and serotonergic systems in rats. | antinociceptiveeffect paracetamol morphine repeatedadministration centralμ receptors.treatment rats injected twice sevendays paracetamol morphine .methods antinociceptive minafter doses paracetamol morphinethrough plate test. toevaluate frontal cortex.results paracetamol morphine antinociceptiveeffect paracetamol maintainedthis seven morphine not.the opioid receptors paracetamol administration morphineproduced progressive opioid receptorswere unaffected. drugs .conclusions opioidergic serotonergic areinvolved ways maintenanceof antinociception paracetamol morphine | non_dup | [] |
2594660 | 10.1007/s00021-007-0248-8 | Linearized stability of incompressible viscous fluid flows in a thin
spherical shell is studied by using the two-dimensional Navier--Stokes
equations on a sphere. The stationary flow on the sphere has two singularities
(a sink and a source) at the North and South poles of the sphere. We prove
analytically for the linearized Navier--Stokes equations that the stationary
flow is asymptotically stable. When the spherical layer is truncated between
two symmetrical rings, we study eigenvalues of the linearized equations
numerically by using power series solutions and show that the stationary flow
remains asymptotically stable for all Reynolds numbers.Comment: 28 pages, 10 figure | Incompressible viscous fluid flows in a thin spherical shell | incompressible viscous fluid flows in a thin spherical shell | linearized incompressible viscous flows spherical navier stokes sphere. stationary sphere singularities sink poles sphere. analytically linearized navier stokes stationary asymptotically stable. spherical truncated symmetrical rings eigenvalues linearized numerically stationary asymptotically reynolds pages | non_dup | [] |
1957644 | 10.1007/s00021-008-0270-5 | We investigate Kato's method for parabolic equations with a quadratic
non-linearity in an abstract form. We extract several properties known from
linear systems theory which turn out to be the essential ingredients for the
method. We give necessary and sufficient conditions for these conditions and
provide new and more general proofs, based on real interpolation. In
application to the Navier-Stokes equations, our approach unifies several
results known in the literature, partly with different proofs. Moreover, we
establish new existence and uniqueness results for rough initial data on
arbitrary domains in ${\mathbb R}^3$ and irregular domains in ${\mathbb R}^n$.Comment: Revised version, to appear in Journal of Mathematical Fluid
Mechanics. New section on solutions in Morrey-spaces added. 35 page | On Kato's method for Navier--Stokes Equations | on kato's method for navier--stokes equations | kato parabolic quadratic linearity form. extract ingredients method. proofs interpolation. navier stokes unifies partly proofs. establish uniqueness rough mathbb irregular mathbb .comment revised mathematical mechanics. morrey added. | non_dup | [] |
2138212 | 10.1007/s00021-011-0071-0 | We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the
$\Z$-periodic case, we establish criteria for recurrence. In the more difficult
$\Z^2$-periodic case, we establish some general results. For a particular
family of $\Z^2$-periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of $\ZZ$-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure | On recurrence and ergodicity for geodesic flows on noncompact periodic
polygonal surfaces | on recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces | recurrence ergodicity billiard noncompact polygonal cocompact establish recurrence. establish results. polygonal restrictions geometric ergodic decomposition directional billiard dense countable directions. ergodicity valued cocycles irrational pages | non_dup | [] |