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

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

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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.