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 $\mathrm{L}_{2,\alpha}=\mathrm{L}_{\alpha}^{2}(\mathbb{R})=\mathrm{L}^{2}(\mathbb{R}, |x|^{2\alpha+1}dx), \alpha>\frac{-1}{2}$.

Keywords