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Proceedings of the American Mathematical Society
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
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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?)

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