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arXiv · 2010.00227

On evolution equations for Lie groupoids

Jean-Marie Lescure·Stéphane Vassout
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Abstract

Using the calculus of Fourier integral operators on Lie groupoids developped in [18], we study the fundamental solution of the evolution equation ($\partial$ $\partial$t + iP)u = 0 where P is a self adjoint elliptic order one G-pseudodifferential operator on the Lie groupoid G. Along the way, we continue the study of distributions on Lie groupoids done in [17] by adding the reduced C *-algebra of G in the picture and we investigate the local nature of the regularizing operators of [32].

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Jean-Marie Lescure, Stéphane Vassout. 2020-10-01. On evolution equations for Lie groupoids. https://arxiv.org/abs/2010.00227

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