Document Type : Research Paper

Authors

• R. Daher
• M. El Hamma

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

• Dunkl operator
• Dunkl transform
• generalized Dunkl translation