Hobson's formula for Dunkl operators and its applications
Nobukazu Shimeno
TL;DR
This paper extends Hobson's formula to Dunkl operators, providing new proofs for classical results in harmonic analysis and special functions, thereby enriching the theoretical framework and applications of Dunkl analysis.
Contribution
The paper introduces a generalized Hobson's formula for Dunkl operators, offering a novel analytical tool and simplified proofs for key results in harmonic analysis and special functions.
Findings
Generalized Hobson's formula for Dunkl operators
Simplified proofs of Maxwell's representation and Pizzetti formula
New insights into harmonic polynomials and Hermite polynomials
Abstract
We generalize classical Hobson's formula concerning partial derivatives of radial functions on a Euclidean space to a formula in the Dunkl analysis. As applications we give new simple proofs of known results involving Maxwell's representation of harmonic polynomials, Bochner-Hecke identity, Pizzetti formula for spherical mean, and Rodrigues formula for Hermite polynomials.
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