dc.identifier.uri |
http://dx.doi.org/10.15488/204 |
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dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/226 |
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dc.contributor.author |
Melo, Severino T.
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dc.contributor.author |
Schick, Thomas
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dc.contributor.author |
Schrohe, Elmar
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dc.date.accessioned |
2016-02-11T09:04:22Z |
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dc.date.available |
2016-02-11T09:04:22Z |
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dc.date.issued |
2006-12-07 |
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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 |
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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 |
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dc.description.sponsorship |
CNPq/306214/2003-2 |
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dc.description.sponsorship |
European Research and Training Network ‘‘Geometric Analysis’/HPRN-CT-1999-0018 |
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dc.language.iso |
eng |
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dc.publisher |
Berlin : Walter de Gruyter |
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dc.relation.ispartofseries |
Journal für die reine und angewandte Mathematik 2006 (2006), Nr. 599 |
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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. |
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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 |
eng |
dc.type |
Article |
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dc.type |
Text |
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dc.relation.essn |
1435-5345 |
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dc.relation.issn |
0075-4102 |
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dc.relation.doi |
http://dx.doi.org/10.1515/CRELLE.2006.083 |
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dc.bibliographicCitation.issue |
599 |
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dc.bibliographicCitation.volume |
2006 |
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dc.bibliographicCitation.firstPage |
217 |
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dc.bibliographicCitation.lastPage |
233 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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