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

Roman A. Veprintsev

doi:10.1515/apam-2014-0053

Published by De Gruyter April 28, 2015

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

Roman A. Veprintsev

From the journal Advances in Pure and Applied Mathematics

https://doi.org/10.1515/apam-2014-0053

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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 𝕊^d-1 constructed in the described manner is fundamental in C(𝕊^d-1). In our construction of functions and proof of the result, we essentially use Dunkl harmonic analysis.

Keywords: Fundamental set; continuous function; unit sphere; Dunkl intertwining operator; κ-spherical harmonics

MSC: 42B35; 42C05; 42C10

Funding source: Russian Foundation for Basic Research

Award Identifier / Grant number: 13-01-00045

Funding source: Ministry of Education and Science of the Russian Federation

Award Identifier / Grant number: 1.1333.2014K

Received: 2014-12-29

Accepted: 2015-3-31

Published Online: 2015-4-28

Published in Print: 2015-7-1