ON EVOLUTION EQUATIONS FOR LIE GROUPOIDS
EQUATIONS D'EVOLUTION SUR LES GROUPOIDES DE LIE
Résumé
Using the calculus of Fourier integral operators on Lie groupoids developped in [18], we study the fundamental solution of the evolution equation (∂ ∂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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