An extension of Pizzetti's formula associated with the Dunkl operators

TL;DR

This paper extends Pizzetti's formula to Dunkl operators, providing an explicit expression for the Dunkl inner product involving harmonic polynomials on the sphere.

Contribution

It introduces a novel extension of Pizzetti's formula specifically tailored for Dunkl operators, enhancing the analytical tools available for Dunkl harmonic analysis.

Findings

Explicit formula for Dunkl inner product derived

Extension applicable to homogeneous Dunkl harmonic polynomials

Advances analytical methods in Dunkl operator theory

Abstract

We give an extension of Pizzetti's formula associated with the Dunkl operators. It gives an explicit formula for the Dunkl inner product of an arbitrary function and a homogeneous Dunkl harmonic polynomial on the unit sphere.