Original Paper

Potential Analysis

, Volume 25, Issue 2, pp 103-119

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

  • Frej ChoucheneAffiliated withDépartement de Mathématiques, Faculté des Sciences de Monastir
  • , Léonard GallardoAffiliated withLaboratoire de Mathématiques et Physique Théorique, CNRS-UMR 6083, Université de Tours Email author 
  • , Maher MiliAffiliated withDépartement de Mathématiques, Faculté des Sciences de Monastir

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

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