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
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