Les équations de la chaleur et de Poisson pour le laplacien généralisé de Jacobi-Dunkl

We show that the heat equation for the Jacobi-Dunkl operator, has a solution in terms of a semigroup of Markovian operators with strictly positive kernel. This result is used to solve the Poisson equation and to introduce a new class of Markov processes on the real line. To cite this article: F. Chouchene et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).