# Three results in Dunkl theory

1 Analyse Mathématique et Applications 2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Abstract : In this article, we establish first a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^p\to L^p$ norm of Dunkl translations in dimension 1. Finally we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.

Keywords : Dunkl operator Paley-Wiener theorem generalized translations

Author: Béchir Amri - Jean-Philippe Anker - Mohamed Sifi -

Source: https://hal.archives-ouvertes.fr/