Pseudodifferential calculus on manifolds with corners and groupoids

1997/07/22 by Monthubert, Bertrand · 3 citations
#19K56 (Secondary) #22A22 (Primary) #35S15 #46L80 #47G30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.funct-an/9707008

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.

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• Lie groupoids, the Satake compactification and the tempered dual, I: The Satake groupoid
• A Volterra Calculus for Lie Groupoids
• An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds

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