Three results in Dunkl analysis

Volume 118 / 2010

Béchir Amri, Jean-Philippe Anker, Mohamed Sifi Colloquium Mathematicum 118 (2010), 299-312 MSC: Primary 33C52; Secondary 42B10, 43A32, 33C80, 22E30. DOI: 10.4064/cm118-1-16


We first establish 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.


  • Béchir AmriDépartement de Mathématiques
    Institut Préparatoire
    aux Études d'Ingénieurs de Tunis (IPEIT)
    1089 Montfleury Tunis, Tunisie
  • Jean-Philippe AnkerLaboratoire MAPMO (UMR 6628)
    Fédération Denis Poisson (FR 2964)
    Université d'Orléans & CNRS Bâtiment de Mathématiques, B.P. 6759
    45067 Orléans Cedex 2, France
  • Mohamed SifiDépartement de Mathématiques
    Faculté des Sciences de Tunis
    Université de Tunis El Manar
    2092 Tunis, Tunisie

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