Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V^{-1}_k$ and ${}^tV_k^{-1}$, and we give some applications.