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

TL;DR

This paper provides alternative proofs for the geometrical Paley-Wiener theorems related to the Dunkl transform and establishes inversion formulas for the Dunkl intertwining operator and its dual, including their distribution representations.

Contribution

It introduces new proofs for the geometrical Paley-Wiener theorems and derives explicit inversion formulas and distribution expressions for the Dunkl intertwining operators.

Findings

Alternative proofs of Paley-Wiener theorems for Dunkl transform

Inversion formulas for Dunkl intertwining operator and its dual

Distribution representations of inverse operators

Abstract

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).