The Hypergroup Associated with the Cherednik Operators and Applications to the Infinitely Divisible Probabilities and Convolution Semigroups

Abstract

In this paper we define the hypergroup \((\mathbb {R}^d, *_\mathcal {H})\) associated with the Cherednik operators on \(\mathbb {R}^d\) and we use the harmonic analysis on this hypergroup to study the infinite divisible probabilities and the convolution semigroups on the hypergroup \((\mathbb {R}^d, *_\mathcal {H})\).