Jackson inequality for Banach spaces on the sphere
type: Item
instance of: scholarly article
title: Jackson inequality for Banach spaces on the sphere
zbMATH Open document ID: 1164.41012
author: Feng Dai
author: Z. Ditzian
published in: Acta Mathematica Hungarica
publication date: 2008-10-21T00:00:00Z
review text: Using certain new moduli of smoothness introduced by \textit{Z.~Ditzian} [J. Anal. Math. 79, 189--200 (1999; Zbl 0981.41004)], the authors prove Jackson estimates for the approximation on the sphere by spherical polynomials. The results are presented separately for even and odd dimensions, where the results for even dimensions are more general. For the former case, a strong converse inequality is given as well.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5355078
zbMATH Keywords: best approximation
zbMATH Keywords: spherical harmonic polynomials
MaRDI profile type: Publication
full work available at URL: s10474-007-6206-3
OpenAlex ID: W1982448974
cites work: Multivariate approximating averages.
cites work: Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques
cites work: Approximation of smooth functions on compact two-point homogeneous spaces
cites work: Best approximation and \(K\)-functionals
cites work: Some equivalence theorems with \(K\)-functionals
cites work: Combinations of multivariate averages
cites work: Fractional derivatives and best approximations
cites work: A modulus of smoothness on the unit sphere
cites work: Jackson-type inequality on the sphere
cites work: Approximation on Banach spaces of functions on the sphere
cites work: Q5556050
DOI: 10.1007/S10474-007-6206-3
description: scientific article; zbMATH DE number 5355078