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

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 599, 2006, Pages 217-233

  Melo, Severino T ^a,b   Schick, Thomas ^a,c   Schrohe, Elmar ^a,d  

^a Universidade de São Paulo ^*

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

^d LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845394647     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2006.083     Document Type: Article

References (12)

1. M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. Math. (2) 87 (1968), 484-530.
2. Louis Bautet de Monvel, Boundary problems for pseudo-differential operators, Acta Math. (1-2) 126 (1971), 11-51.
3. B. V. Fedosov, Index theorems, in: Partial differential equations, VIII, Encyclop. Math. Sci. 65, Springer, Berlin (1996), 155-251.
4. G. Grubb, Functional Calculus of Pseudodifferential Boundary Problems, Second Edition, Birkhäuser, Boston 1996.
5. G. Grubb and G. Geymonat, The essential spectrum of elliptic systems of mixed order, Math. Ann. 227 (1977), 247-276.
6. J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305.
7. S. T. Melo, R. Nest, and E. Schrohe, C*-structure and K-theory of Boutet de Monvel's algebra, J. reine angew. Math. 561 (2003), 145-175.
8. S. Rempel and B.-W. Schulze, Index theory of elliptic boundary problems, Akademie-Verlag, Berlin 1982.
9. M. Rørdam, F. Larsen, and N. J. Laustsen, An Introduction to K-Theory for C*-Algebras, London Math. Soc. Stud. Texts 49, Cambridge University Press, Cambridge 2000.
10. E. Schrohe, Fréchet algebra techniques for boundary value problems on noncompact manifolds: Fredholm criteria and functional calculus via spectral invariance, Math. Nachr. 199 (1999), 145-185.
11. E. Schrohe, A short introduction to Boutet de Monvel's calculus, Approaches to Singular Analysis (Berlin 1999), Oper. Th. Adv. Appl. 125, Birkhäuser, Basel (2001), 85-116.
12. N. E. Wegge-Olsen, K-theory and C*-algebras, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York 1993.