An analog of Titchmarsh's theorem for the Dunkl transform in the space $mathrm{L}_{alpha}^{2}(mathbb{R})$

Authors

Department of Mathematics, Faculty of Science Ain Chick, University Hassan II, Casablanca, Morocco

Abstract

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

Keywords