Pseudodifferential Subspaces and Their Applications in Elliptic Theory
Identifieur interne : 000F70 ( Istex/Corpus ); précédent : 000F69; suivant : 000F71Pseudodifferential Subspaces and Their Applications in Elliptic Theory
Auteurs : Anton Savin ; Boris SterninSource :
- Trends in Mathematics ; 2006.
Abstract
Abstract: The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah73-Patodi— Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.
Url:
DOI: 10.1007/978-3-7643-7687-1_12
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ISTEX:4D5BE519050144A232FD2C49C739DD1BB5CF6D55Le document en format XML
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Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah73-Patodi— Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. 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Vlasyevskiy pereulok, d. 11</Street><Postcode>119002</Postcode><City>Moscow</City><Country>Russia</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah73-Patodi— Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>elliptic operator</Keyword><Keyword>boundary value problem</Keyword><Keyword>pseudodifferential subspace</Keyword><Keyword>dimension functional</Keyword><Keyword><Emphasis Type="Italic">η</Emphasis>-invariant</Keyword><Keyword>index</Keyword><Keyword>mod<Emphasis Type="Italic">n</Emphasis>-index</Keyword><Keyword>parity condition</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>The work was partially supported by RFBR grants NN 05-01-00982, 03-02-16336, 06-01-00098 and presidential grant MK-1713.2005.1.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Pseudodifferential Subspaces and Their Applications in Elliptic Theory</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Pseudodifferential Subspaces and Their Applications in Elliptic Theory</title></titleInfo><name type="personal"><namePart type="given">Anton</namePart><namePart type="family">Savin</namePart><affiliation>Independent University of Moscow, B. 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Vlasyevskiy pereulok, d. 11, 119002, Moscow, Russia</affiliation><affiliation>E-mail: sternin@mail.ru</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Birkhäuser Basel</publisher><place><placeTerm type="text">Basel</placeTerm></place><dateIssued encoding="w3cdtf">2006</dateIssued><dateIssued encoding="w3cdtf">2006</dateIssued><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah73-Patodi— Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.</abstract><relatedItem type="host"><titleInfo><title>C*-algebras and Elliptic Theory</title></titleInfo><name type="personal"><namePart type="given">Bogdan</namePart><namePart type="family">Bojarski</namePart><affiliation>Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckih 8, 00-956, Warszawa, Poland</affiliation><affiliation>E-mail: bojarski@impan.gov.pl</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Alexander</namePart><namePart type="given">S.</namePart><namePart type="family">Mishchenko</namePart><affiliation>Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119992, Moscow, Russia</affiliation><affiliation>E-mail: asmish@mech.math.msu.su</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Evgenij</namePart><namePart type="given">V.</namePart><namePart type="family">Troitsky</namePart><affiliation>Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119992, Moscow, Russia</affiliation><affiliation>E-mail: troitsky@mech.math.msu.su</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Andrzej</namePart><namePart type="family">Weber</namePart><affiliation>Instytut Matematyki, Uniwersytet Warszawski, Banacha 2, 02-097, Warszawa, Poland</affiliation><affiliation>E-mail: aweber@mimuw.edu.pl</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Collection of essays" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2006</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="M">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="M12066">Functional Analysis</topic></subject><identifier type="DOI">10.1007/978-3-7643-7687-1</identifier><identifier type="ISBN">978-3-7643-7686-4</identifier><identifier type="eISBN">978-3-7643-7687-1</identifier><identifier type="BookTitleID">133532</identifier><identifier type="BookID">978-3-7643-7687-1</identifier><identifier type="BookChapterCount">14</identifier><identifier type="BookSequenceNumber">36</identifier><part><date>2006</date><detail type="volume"><number>2006</number><caption>vol.</caption></detail><extent unit="pages"><start>247</start><end>289</end></extent></part><recordInfo><recordOrigin>Birkhäuser Verlag, 2006</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Trends in Mathematics</title></titleInfo><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2006</copyrightDate><issuance>serial</issuance></originInfo><identifier type="SeriesID">4961</identifier><recordInfo><recordOrigin>Birkhäuser Verlag, 2006</recordOrigin></recordInfo></relatedItem><identifier type="istex">4D5BE519050144A232FD2C49C739DD1BB5CF6D55</identifier><identifier type="ark">ark:/67375/HCB-B81HH4SK-F</identifier><identifier type="DOI">10.1007/978-3-7643-7687-1_12</identifier><identifier type="ChapterID">12</identifier><identifier type="ChapterID">Chap12</identifier><accessCondition type="use and reproduction" contentType="copyright">Birkhäuser Verlag, 2006</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Birkhäuser Verlag Basel/Switzerland, 2006</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/4D5BE519050144A232FD2C49C739DD1BB5CF6D55/metadata/json</uri></json:item></metadata><annexes><json:item><extension>txt</extension><original>true</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/4D5BE519050144A232FD2C49C739DD1BB5CF6D55/annexes/txt</uri></json:item></annexes></istex></record>Pour manipuler ce document sous Unix (Dilib)
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