About the convolution of distributions on groupoids

  • Jean-Marie Lescure

    Université Blaise Pascal, Aubière, France
  • Dominique Manchon

    Université Blaise Pascal, Aubière, France
  • Stéphane Vassout

    Institut de Mathématiques de Jussieu - Paris Rive Gauche, France

Abstract

We review the properties of transversality of distributions with respect to submersions. This allows us to construct a convolution product for a large class of distributions on Lie groupoids. We get a unital involutive algebra enlarging the convolution algebra associated with any Lie groupoid . We prove that -operators are convolution operators by transversal distributions. We also investigate the microlocal aspects of the convolution product. We give sufficient conditions on wave front sets to compute the convolution product and we show that the wave front set of the convolution product of two distributions is essentially the product of their wave front sets in the symplectic groupoid of Coste–Dazord–Weinstein. This also leads to a subalgebra of which contains for instance the algebra of pseudodifferential -operators and a class of Fourier integral -operators which will be the central theme of a forthcoming paper.

Cite this article

Jean-Marie Lescure, Dominique Manchon, Stéphane Vassout, About the convolution of distributions on groupoids. J. Noncommut. Geom. 11 (2017), no. 2, pp. 757–789

DOI 10.4171/JNCG/11-2-10