(1) Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia;(2) Laboratoire de Mathématiques et Physique Théorique, CNRS-UMR 6083, Université de Tours, Campus de Grandmont, 37200 Tours, France
Abstract:
This paper is devoted to the heat equation associated with the Jacobi–Dunkl operator on the real line. In particular we show that the heat semigroup has a strictly positive kernel and a finite Green operator. As a direct application, we solve the Poisson equation and we introduce a new family of one-dimensional Markov processes.