Potential Analysis

, Volume 25, Issue 2, pp 103–119

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

Original Paper

DOI: 10.1007/s11118-006-9012-6

Cite this article as:
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.

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 

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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