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

Mohamed, Elhamma; Lahlai, Hind; Daher, Radouan

Manuscript ID : 521887 Visit : 43 Page: 127 - 131

Article Type: Original Research

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 ()

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

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