Another proofs of the geometrical forms of Paley-Wiener theorems for the Dunkl transform and inversion formulas for the Dunkl interwining operator and for its dual

In this paper we present another proofs of the geometrical forms of Paley-Wiener theorems for the Dunkl transform given in [15], and we prove inversion formulas for the Dunl interwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators vk(-1) and tvk(-1).