, Volume 25, Issue 2, pp 103-119
Date: 15 Jul 2006

The Heat Semigroup for the Jacobi–Dunkl Operator and the Related Markov Processes

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.