2020/10/01 by Lescure, Jean-Marie, Vassout, Stéphane · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2010.00227
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].