The Heat Semigroup for the Jacobi–Dunkl Operator and the Related Markov Processes
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- Chouchene, F., Gallardo, L. & Mili, M. Potential Anal (2006) 25: 103. doi:10.1007/s11118-006-9012-6
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.