Index theory for boundary value problems via continuous fields of C*-algebras

Journal of Functional Analysis

Volumn 257, Issue 8, 2009, Pages 2645-2692

  Aastrup, Johannes ^a   Nest, Ryszard ^b   Schrohe, Elmar ^c  

^a SFB 478 Geometrische Strukturen ^*  (Germany)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Boundary value problems; Continuous fields of C* algebras; Groupoids; Index theory

Indexed keywords

EID: 68949184855     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.04.019     Document Type: Article

References (15)

1. *-algebras and the tangent groupoid for manifolds with boundary. J. Funct. Anal. 237 (2006) 482-506
2. Boutet de Monvel L. Boundary problems for pseudo-differential operators. Acta Math. 126 (1971) 11-51
3. Connes A. Noncommutative Geometry (1994), Academic Press, San Diego
4. Elliott G., Natsume T., and Nest R. The Atiyah-Singer index theorem as passage to the classical limit in quantum mechanics. Comm. Math. Phys. 182 (1996) 505-533
5. Fedosov B.V. Index Theorems. Partial Differential Equations VIII. Encyclopaedia Math. Sci. vol. 65 (1996), Springer, Berlin 155-251 translation from Itogi Nauki Tekh.
6. Fedosov B.V. Index Theorems. Sovrem. Mat. Fundam. Napravl. 65 (1991) 165-268
7. Grubb G. Functional Calculus of Pseudodifferential Boundary Problems. second ed. (1996), Birkhäuser, Boston
8. Kumano-go H. Pseudo-Differential Operators (1981), MIT Press, Cambridge/London
9. *-structure and K-theory of Boutet de Monvel's algebra. J. Reine Angew. Math. 561 (2003) 145-175
10. Melo S., Schick T., and Schrohe E. A K-theoretic proof of Boutet de Monvel's index theorem. J. Reine Angew. Math. 599 (2006) 217-233
11. Rempel S., and Schulze B.-W. Index Theory of Elliptic Boundary Problems (1982), Akademie-Verlag, Berlin
12. p Sobolev spaces. Integral Equations Operator Theory 13 (1990) 271-284
13. Schrohe E. Fréchet algebra techniques for boundary value problems on noncompact manifolds: Fredholm criteria and functional calculus via spectral invariance. Math. Nachr. 199 (1999) 145-185
14. Schrohe E. A short introduction to Boutet de Monvel's calculus. In: Gil J., Grieser D., and Lesch M. (Eds). Approaches to Singular Analysis. Oper. Theory Adv. Appl. vol. 125 (2001) 85-116
15. Schrohe E., and Schulze B.-W. Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities I. Pseudo-Differential Calculus and Mathematical Physics. Math. Top. vol. 5 (1994), Akademie-Verlag, Berlin 97-209