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

2020/06/05 by Nobukazu Shimeno, Shimeno, Nobukazu, Naoya Tani +1
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2006.03223

openalex publication_date 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Mean value property associated with the Dunkl Laplacian

Related

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• An introduction to Dunkl theory and its analytic aspects
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• Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type
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