A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems

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dc.identifier.uri http://dx.doi.org/10.15488/204
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/226
dc.contributor.author Melo, Severino T.
dc.contributor.author Schick, Thomas
dc.contributor.author Schrohe, Elmar
dc.date.accessioned 2016-02-11T09:04:22Z
dc.date.available 2016-02-11T09:04:22Z
dc.date.issued 2006-12-07
dc.identifier.citation Melo, Severino T.; Schick, Thomas; Schrohe, Elmar: A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems. In: Journal für die reine und angewandte Mathematik 2006 (2006), Nr. 599, S. 217-233. DOI: http://dx.doi.org/10.1515/CRELLE.2006.083
dc.description.abstract We study the C*-closure U of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with boundary partial derivative X not equal phi. We find short exact sequences in K-theory 0 -> K-i (C(X)) -> K-i(U/R) ->(P) K1-i(C-0(T*X degrees)) -> 0, i = 0,1, which split, so that K-i(U/R) congruent to K-i(C(X)) circle plus K1-i(Co(T*X degrees)). Using only simple K-theoretic arguments and the Atiyah-Singer index theorem, we show that the Fredhohn index of an elliptic element in A is given by ind A = ind(t)(p[A])), where [A] is the class of A in K-1(U/R) and ind(t) is the topological index, a relation first established by Boutet de Monvel by different methods. eng
dc.description.sponsorship CNPq/452780/2003-9
dc.description.sponsorship CNPq/306214/2003-2
dc.description.sponsorship European Research and Training Network ‘‘Geometric Analysis’/HPRN-CT-1999-0018
dc.language.iso eng
dc.publisher Berlin : Walter de Gruyter
dc.relation.ispartofseries Journal für die reine und angewandte Mathematik 2006 (2006), Nr. 599
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject algebra eng
dc.subject operators eng
dc.subject calculus eng
dc.subject.ddc 510 | Mathematik ger
dc.title A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems
dc.type article
dc.type Text
dc.relation.essn 1435-5345
dc.relation.issn 0075-4102
dc.relation.doi http://dx.doi.org/10.1515/CRELLE.2006.083
dc.bibliographicCitation.issue 599
dc.bibliographicCitation.volume 2006
dc.bibliographicCitation.firstPage 217
dc.bibliographicCitation.lastPage 233
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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