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

Document Type : Research Paper


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


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


  • Receive Date: 14 January 2012
  • Revise Date: 07 February 2012
  • Accept Date: 21 February 2012