An elementary proof of the positivity of the intertwining operator in one-dimensional trigonometric Dunkl theory

TL;DR

This paper provides a straightforward integral expression for the intertwining operator in one-dimensional trigonometric Dunkl theory and proves its positivity, simplifying previous approaches.

Contribution

It introduces a simple integral formula for the intertwining operator and establishes its positivity in the one-dimensional trigonometric Dunkl setting.

Findings

Derived a simple integral expression for the intertwining operator

Proved the positivity of the intertwining operator

Simplified understanding of the operator's properties in Dunkl theory

Abstract

This note is devoted to the intertwining operator in the one--dimensional trigonometric Dunkl setting. We obtain a simple integral expression of this operator and deduce its positivity.