Pseudodifferential Subspaces and Their Applications in Elliptic Theory
Identifieur interne : 000F70 ( Istex/Curation ); précédent : 000F69; suivant : 000F71Pseudodifferential Subspaces and Their Applications in Elliptic Theory
Auteurs : Anton Savin [Russie] ; Boris Sternin [Russie]Source :
- 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
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :000F70
Links to Exploration step
ISTEX:4D5BE519050144A232FD2C49C739DD1BB5CF6D55Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Pseudodifferential Subspaces and Their Applications in Elliptic Theory</title>
<author><name sortKey="Savin, Anton" sort="Savin, Anton" uniqKey="Savin A" first="Anton" last="Savin">Anton Savin</name>
<affiliation wicri:level="1"><mods:affiliation>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow, Russia</mods:affiliation>
<country xml:lang="fr">Russie</country>
<wicri:regionArea>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: antonsavin@mail.ru</mods:affiliation>
<country wicri:rule="url">Russie</country>
</affiliation>
</author>
<author><name sortKey="Sternin, Boris" sort="Sternin, Boris" uniqKey="Sternin B" first="Boris" last="Sternin">Boris Sternin</name>
<affiliation wicri:level="1"><mods:affiliation>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow, Russia</mods:affiliation>
<country xml:lang="fr">Russie</country>
<wicri:regionArea>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: sternin@mail.ru</mods:affiliation>
<country wicri:rule="url">Russie</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:4D5BE519050144A232FD2C49C739DD1BB5CF6D55</idno>
<date when="2006" year="2006">2006</date>
<idno type="doi">10.1007/978-3-7643-7687-1_12</idno>
<idno type="url">https://api.istex.fr/document/4D5BE519050144A232FD2C49C739DD1BB5CF6D55/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000F70</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000F70</idno>
<idno type="wicri:Area/Istex/Curation">000F70</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Pseudodifferential Subspaces and Their Applications in Elliptic Theory</title>
<author><name sortKey="Savin, Anton" sort="Savin, Anton" uniqKey="Savin A" first="Anton" last="Savin">Anton Savin</name>
<affiliation wicri:level="1"><mods:affiliation>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow, Russia</mods:affiliation>
<country xml:lang="fr">Russie</country>
<wicri:regionArea>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: antonsavin@mail.ru</mods:affiliation>
<country wicri:rule="url">Russie</country>
</affiliation>
</author>
<author><name sortKey="Sternin, Boris" sort="Sternin, Boris" uniqKey="Sternin B" first="Boris" last="Sternin">Boris Sternin</name>
<affiliation wicri:level="1"><mods:affiliation>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow, Russia</mods:affiliation>
<country xml:lang="fr">Russie</country>
<wicri:regionArea>Independent University of Moscow, B. Vlasyevskiy pereulok, d. 11, 119002, Moscow</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: sternin@mail.ru</mods:affiliation>
<country wicri:rule="url">Russie</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s">Trends in Mathematics</title>
<imprint><date>2006</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml: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.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000F70 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Curation/biblio.hfd -nk 000F70 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Istex |étape= Curation |type= RBID |clé= ISTEX:4D5BE519050144A232FD2C49C739DD1BB5CF6D55 |texte= Pseudodifferential Subspaces and Their Applications in Elliptic Theory }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |