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

Abstract

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

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/