Three results in Dunkl theory

Béchir Amri (1) , Jean-Philippe Anker (2) , Mohamed Sifi (1)

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

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.

Mots clés: Dunkl operator; Paley-Wiener theorem; generalized translations

Domaines: Analyse classique [math.CA]

Béchir Amri, Jean-Philippe Anker, Mohamed Sifi. Three results in Dunkl theory. 2009. ⟨hal-00377674v1⟩