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The strong converse inequality for de la Vallée Poussin means on the sphere.
- Source :
-
Journal of Computational Analysis & Applications . Jan2016, Vol. 20 Issue 1, p34-41. 8p. - Publication Year :
- 2016
-
Abstract
- This paper discusses the approximation by de la Vallée Poussin means Vnf on the unit sphere. Especially, the lower bound of approximation is studied. As a main result, the strong converse inequality for the means is established. Namely, it is proved that there are constants C1 and C2 such that C1ω (f, 1/√n) p ≤ ‖Vnf - f‖p ≤ C2ω (f, 1/√n) p for any p-th Lebesgue integrable or continuous function f defined on the sphere, where ω(f, t)p is the modulus of smoothness of f. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 20
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 111203966