Pseudodifferential calculus on manifolds with corners and groupoids
HTML articles powered by AMS MathViewer
- by Bertrand Monthubert PDF
- Proc. Amer. Math. Soc. 127 (1999), 2871-2881 Request permission
Erratum: Proc. Amer. Math. Soc. 128 (2000), 627-627.
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
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530. MR 236950, DOI 10.2307/1970715
- Alain Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994. MR 1303779
- 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.
- Richard B. Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics, vol. 4, A K Peters, Ltd., Wellesley, MA, 1993. MR 1348401, DOI 10.1016/0377-0257(93)80040-i
- Richard B. Melrose and Victor Nistor, $K$-theory of $b$-pseudodifferential operators and an $\mathbb {R}^k$-equivariant index theorem, Preprint.
- Bertrand Monthubert and François Pierrot, Indice analytique et groupoïdes de lie, C.R. Acad. Sci. Paris Ser. I, 325, No. 2, 193-198 (1997).
- Victor Nistor, Alan Weinstein, and Ping Xu, Pseudodifferential operators on differential groupoids, Preprint.
- Alan Weinstein, Groupoids: unifying internal and external symmetry. A tour through some examples, Notices Amer. Math. Soc. 43 (1996), no. 7, 744–752. MR 1394388
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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2871-2881
- MSC (1991): Primary 35S15, 47G30, 22A22; Secondary 46L80, 19K56
- DOI: https://doi.org/10.1090/S0002-9939-99-04850-9
- MathSciNet review: 1600121