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Licensed Unlicensed Requires Authentication Published by De Gruyter April 28, 2015

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

  • Roman A. Veprintsev EMAIL logo


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

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

© 2015 by De Gruyter

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