GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE DUNKL TRANSFORM IN THE SPACE $L^P(R)$

Subject Areas : International Journal of Mathematical Modelling & Computations

Elhamma Mohamed ¹ , Hind Lahlai ² , Radouan Daher ³

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Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

Keywords: Dunkl operator, Dunkl transform, generalized translation Dunkl operator,

Abstract :

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(\psi,p)$-Lipschitz Dunkl condition in the space $\mathrm{L}_{p,\alpha}=\mathrm{L}^{p}(\mathbb{R},|x|^{2\alpha+1}dx)$‎, ‎where $\alpha>-\frac{1}{2}$.