Representation of Generalized Translations of the Product of Two Functions on Signed Hypergroups on the Real Line

Abstract

In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hypergroups on $\mathbf{R}$. Especially, we study the representation of the generalized translations of the product of two functions for these signed hypergroups.