Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Pseudodifferential calculus on manifolds
with corners and groupoids

Author: Bertrand Monthubert
Journal: Proc. Amer. Math. Soc. 127 (1999), 2871-2881
MSC (1991): Primary 35S15, 47G30, 22A22; Secondary 46L80, 19K56
Published electronically: April 23, 1999
Erratum: Proc. Amer. Math. Soc. 128 (1999), no. 2, 627 - 627.
MathSciNet review: 1600121
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $b$-calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing operators of the (small) $b$-calculus.

References [Enhancements On Off] (What's this?)

  • 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, $K$-theory of $b$-pseudodifferential operators and an $\mathbb{R}^k$-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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35S15, 47G30, 22A22, 46L80, 19K56

Retrieve articles in all journals with MSC (1991): 35S15, 47G30, 22A22, 46L80, 19K56

Additional Information

Bertrand Monthubert
Affiliation: Laboratoire Emile Picard, UFR MIG, Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France

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
Published electronically: April 23, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society