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

TL;DR

This paper derives inversion formulas for the Dunkl intertwining operator and its dual, providing explicit expressions for their inverse operators and exploring applications in function and distribution spaces.

Contribution

It introduces new inversion formulas for the Dunkl intertwining operator and its dual, along with explicit representations of their inverses in distribution spaces.

Findings

Derived explicit inversion formulas for V_k and its dual.

Expressed the inverse operators as distributions.

Applied results to specific function and distribution spaces.

Abstract

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 $V_k^{-1}$ and ${}^tV_k^{-1}$, and we give some applications.