Potential Analysis

, Volume 25, Issue 2, pp 103–119 | Cite as

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

Original Paper


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.

Key words

Jacobi–Dunkl operator heat semigroup generalized Fourier transform Poisson's equation Markov processes 

Mathematics Subject Classification (2000)

42A76 47D07 31A35 58J35 60J25 34K60 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Département de MathématiquesFaculté des Sciences de MonastirMonastirTunisia
  2. 2.Laboratoire de Mathématiques et Physique ThéoriqueCNRS-UMR 6083, Université de ToursToursFrance

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