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The Heat Semigroup for the Jacobi–Dunkl Operator and the Related Markov Processes |
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| Authors: | Frej Chouchene Léonard Gallardo Maher Mili |
| Institution: | (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. |
| Keywords: | Jacobi– Dunkl operator heat semigroup generalized Fourier transform Poisson's equation Markov processes |
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