Article
Licensed
Unlicensed
Requires Authentication
Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
-
Roman A. Veprintsev
Published/Copyright:
April 28, 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 đd-1 constructed in the described manner is fundamental in C(đd-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; Îș-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
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- 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
Keywords for this article
Fundamental set;
continuous function;
unit sphere;
Dunkl intertwining operator;
Îș-spherical harmonics
Articles in the same Issue
- 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
