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Pseudodifferential calculus on manifolds with corners and groupoids
Author(s):
Bertrand
Monthubert
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2871-2881.
MSC (1991):
Primary 35S15, 47G30, 22A22;
Secondary 46L80, 19K56
Posted:
April 23, 1999
Errata:
Proc. Amer. Math. Soc. 128 (1999), no. 2, 627 - 627.
MathSciNet review:
1600121
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Abstract:
We build a longitudinally smooth, differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called  -calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing operators of the (small)  -calculus.
References:
- 1.
- M. F. Atiyah and I. M. Singer, The index of elliptic operators, I, Annals of Math. 87 (1968), 484-530. MR 38:5243
- 2.
- Alain Connes, Noncommutative Geometry, Academic Press, Inc., 1994. MR 95j:46063
- 3.
- Lars Hörmander, The analysis of linear partial differential operators III: Pseudo-differential operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1994.
- 4.
- Richard B. Melrose, The Atiyah-Patodi-Singer index theorem, A. K. Peters, 1993. MR 96g:58180
- 5.
- Richard B. Melrose and Victor Nistor,
 -theory of  -pseudodifferential operators and an  -equivariant index theorem, Preprint. - 6.
- Bertrand Monthubert and François Pierrot, Indice analytique et groupoïdes de lie, C.R. Acad. Sci. Paris Ser. I, 325, No. 2, 193-198 (1997).
- 7.
- Victor Nistor, Alan Weinstein, and Ping Xu, Pseudodifferential operators on differential groupoids, Preprint.
- 8.
- A. Weinstein, Groupoids: unifying internal and external symmetry, Notices Amer. Math. Soc. 43 (1996), 744-752. MR 97f:20072
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Additional Information:
Bertrand
Monthubert
Affiliation:
Laboratoire Emile Picard, UFR MIG, Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France
Email:
monthube@picard.ups_rlse.fr
DOI:
10.1090/S0002-9939-99-04850-9
PII:
S 0002-9939(99)04850-9
Keywords:
Pseudodifferential calculus,
manifolds with corners,
groupoids,
$C^*$-algebras
Received by editor(s):
September 16, 1997
Received by editor(s) in revised form:
December 3, 1997
Posted:
April 23, 1999
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
1999,
American Mathematical Society
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