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On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

Abdelkefi, ChokriSifi, Mohamed — 2006

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30 In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space. * Supported by 04/UR/15-02.

Three results in Dunkl analysis

Béchir AmriJean-Philippe AnkerMohamed Sifi — 2010

Colloquium Mathematicae

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 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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