The Transmutation Operators Relating to a Dunkl Type Operator on $${\mathbb{R}}$$ R and Their Positivity

Abstract

In this paper we prove the positivity of the transmutation operators relating to a Dunkl type operator on the real line, and we deduce the positivity of the transmutation operators associated with the Jacobi–Dunkl operator on \({\mathbb{R}}\) proved in Chouchane et al. (Anal Appl 1(4):387–412, 2003).