Generalization of Titchmarsh s Theorem for the Jacobi-Dunkl Transform

In this paper, using a generalized Jacobi-Dunkl translation operator, we prove a generalization of Titchmarsh s theorem for functions in the k-Jacobi-Dunkl-Lipschitz class defined by the finite differences of order k ∈ N* and Sobolev spaces associated with the Jacobi-Dunkl operator.