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Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
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Roman A. Veprintsev
Veröffentlicht/Copyright:
28. April 2015
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 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.
Keywords: Fundamental set; continuous function; unit sphere; Dunkl intertwining operator; κ-spherical harmonics
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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Artikel in diesem Heft
- Frontmatter
- Variations on a theorem of Beurling
- Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
- Boundary behavior of Green function for a parabolic equation in bounded domain
- On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle
- Some properties of chain recurrent sets in a nonautonomous discrete dynamical system
- A joint generalization of Van Vleck's and Kannappan's equations on groups
Schlagwörter für diesen Artikel
Fundamental set;
continuous function;
unit sphere;
Dunkl intertwining operator;
κ-spherical harmonics
Artikel in diesem Heft
- Frontmatter
- Variations on a theorem of Beurling
- Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
- Boundary behavior of Green function for a parabolic equation in bounded domain
- On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle
- Some properties of chain recurrent sets in a nonautonomous discrete dynamical system
- A joint generalization of Van Vleck's and Kannappan's equations on groups
