Generalization of Titchmarsh's Theorem for the Dunkl Transform

Subject Areas : International Journal of Mathematical Modelling & Computations

salah El ouadih ¹ , Radouan Daher ²

1 - university
2 - .

Received: 2016-07-27 Accepted : 2016-11-28 Published : 2016-11-01

Keywords: Dunkl transform, Dunkl kernel, generalized spherical mean operator,

Abstract :

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.