Generalized Dunkl–Opdam Operator and its Properties in the Spaces of Functions Analytic in Domains

Abstract

We define the generalized Dunkl–Opdam operator and study some of its properties in the space ℋ(G) of functions analytic in an arbitrary domain G . We also investigate the possibility of extension of a diagonal operator constructed by the Taylor coefficients of generalized hypergeometric function to the space ℋ(G).