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

Roman Veprintsev

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arXiv · 1602.04594

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

Roman Veprintsev

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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 $\mathbb{S}^{d-1}$ 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.

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BibTeX RIS

Roman Veprintsev. 2016-02-15. Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere. https://arxiv.org/abs/1602.04594

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