ABOUT THE CONVOLUTION OF DISTRIBUTIONS ON GROUPOIDS - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Journal of Noncommutative Geometry Année : 2017

ABOUT THE CONVOLUTION OF DISTRIBUTIONS ON GROUPOIDS

Résumé

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 $\cE_{r,s}'(G,\Omega^{1/2})$ enlarging the convolution algebra $C^\infty_c(G,\Omega^{1/2})$ associated with any Lie groupoid $G$. We prove that $G$-operators are convolution operators by transversal distributions. We also investigate the microlocal aspects of the convolution product. We give conditions on wave front sets sufficient 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 $T^*G$ of Coste-Dazord-Weinstein. This also leads to a subalgebra $\cE_{a}'(G,\Omega^{1/2})$ of $\cE_{r,s}'(G,\Omega^{1/2})$ which contains for instance the algebra of pseudodifferential $G$-operators and a class of Fourier integral $G$-operators which will be the central theme of a forthcoming paper.
Fichier principal
Vignette du fichier
CODIGRO_v5.pdf (382.31 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01113881 , version 1 (06-02-2015)
hal-01113881 , version 2 (01-06-2015)
hal-01113881 , version 3 (06-11-2015)
hal-01113881 , version 4 (27-11-2019)

Identifiants

Citer

Jean-Marie Lescure, Dominique Manchon, Stéphane Vassout. ABOUT THE CONVOLUTION OF DISTRIBUTIONS ON GROUPOIDS. Journal of Noncommutative Geometry, 2017, 11 (2), pp.757-789. ⟨10.4171/JNCG/11-2-10⟩. ⟨hal-01113881v4⟩
262 Consultations
505 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More