Some results for the Jacobi-Dunkl transform in the space  $L^{2}(\mathbb{R},A_{\alpha,\beta}(t)dt)$

S. EL OUADIHa,* , R. DAHERb and A. BELKHADIRc

Some results for the Jacobi-Dunkl transform in the space $L^{2}(\mathbb{R},A_{\alpha,\beta}(t)dt)$

Authors :

S. EL OUADIH^a,*, R. DAHER^band A. BELKHADIR^c

Author Address :

^a,b,cDepartement of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II, Casablanca, Morocco.

*Corresponding author.

Abstract :

In this paper, using a generalized Jacobi-Dunkl translation operator, we prove an analog of Titchmarsh’s theorem for functions satisfying the Jacobi-Dunkl Lipschitz condition in $L^{2}(\mathbb{R},A_{\alpha,\beta}(t)dt)$, $\alpha\geq\beta\geq\frac{-1}{2}$, $\alpha\neq\frac{-1}{2}$.

Keywords :

Jacobi-Dunkl operator, Jacobi-Dunkl transform, generalized Jacobi-Dunkl translation.

DOI :

Article Info :

Received : June 09, 2015; Accepted : September 21, 2015.