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Pseudodifferential calculus on manifolds with corners and groupoids

Bertrand Monthubert
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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 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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Bertrand Monthubert. 1997-07-25. Pseudodifferential calculus on manifolds with corners and groupoids. https://arxiv.org/abs/funct-an/9707008

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