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Three results in Dunkl theory

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.
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Béchir Amri, Jean-Philippe Anker, Mohamed Sifi. Three results in Dunkl theory. Colloq. Math., 2010, 118 (1), pp.299-312. ⟨10.4064/cm118-1-16⟩. ⟨hal-00377674v2⟩

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