Details
| Original language | English |
|---|---|
| Pages (from-to) | 217-233 |
| Number of pages | 17 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Issue number | 599 |
| Early online date | 2005 |
| Publication status | Published - 2006 |
Abstract
We study the C*-closure 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 . We find short exact sequences in K-theory which split, so that K i( ) ≅ K i(C(X)) ⊕ K 1-i(C 0(T*X°)). Using only simple K-theoretic arguments and the Atiyah-Singer index theorem, we show that the Fredholm index of an elliptic element in is given by where [A] is the class of A in K 1( ) and ind t is the topological index, a relation first established by Boutet de Monvel by different methods.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal fur die Reine und Angewandte Mathematik, No. 599, 2006, p. 217-233.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems
AU - Melo, Severino T.
AU - Schick, Thomas
AU - Schrohe, Elmar
N1 - Funding Information: Acknowledgments. Severino Melo was supported by the Brazilian agency CNPq (Processos 452780/2003-9 and 306214/2003-2). Elmar Schrohe had support from the European Research and Training Network ‘‘Geometric Analysis’’ (Contract HPRN-CT-1999-0018). He thanks Johannes Aastrup and Ryszard Nest for several helpful discussions. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - We study the C*-closure 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 . We find short exact sequences in K-theory which split, so that K i( ) ≅ K i(C(X)) ⊕ K 1-i(C 0(T*X°)). Using only simple K-theoretic arguments and the Atiyah-Singer index theorem, we show that the Fredholm index of an elliptic element in is given by where [A] is the class of A in K 1( ) and ind t is the topological index, a relation first established by Boutet de Monvel by different methods.
AB - We study the C*-closure 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 . We find short exact sequences in K-theory which split, so that K i( ) ≅ K i(C(X)) ⊕ K 1-i(C 0(T*X°)). Using only simple K-theoretic arguments and the Atiyah-Singer index theorem, we show that the Fredholm index of an elliptic element in is given by where [A] is the class of A in K 1( ) and ind t is the topological index, a relation first established by Boutet de Monvel by different methods.
UR - http://www.scopus.com/inward/record.url?scp=33845394647&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2006.083
DO - 10.1515/CRELLE.2006.083
M3 - Article
AN - SCOPUS:33845394647
SP - 217
EP - 233
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 599
ER -