Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere

DOI10.1515/APAM-2014-0053zbMATH Open1347.42048arXiv1602.04594OpenAlexW2963709976MaRDI QIDQ2515419

R. A. Veprintsev

Publication date: 5 August 2015

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

Abstract: We establish a necessary and sufficient condition on a continuous function on $[-1,1]$ under which the family of functions on the unit sphere $mathbb{S}^{d-1}$ constructed in the described manner is fundamental in $C(mathbb{S}^{d-1})$. In our construction of functions and proof of the result, we essentially use Dunkl harmonic analysis.

Full work available at URL: https://arxiv.org/abs/1602.04594

zbMATH Keywords

unit spherecontinuous functionsDunkl intertwining operatorfundamental set\(\kappa\)-spherical harmonicsDunkl harmonic analysis

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Harmonic analysis in several variables (42B99)

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