ON EVOLUTION EQUATIONS FOR LIE GROUPOIDS

EQUATIONS D'EVOLUTION SUR LES GROUPOIDES DE LIE

Jean-Marie Lescure (1) , Stéphane Vassout (2)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
2 IMJ - Institut de Mathématiques de Jussieu

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].

Domaines: Algèbres d'opérateurs [math.OA]; Géométrie différentielle [math.DG]

Jean-Marie Lescure, Stéphane Vassout. ON EVOLUTION EQUATIONS FOR LIE GROUPOIDS. 2020. ⟨hal-02953626⟩