Strong uniform approximation by double Fourier series
type: Item
instance of: scholarly article
title: Strong uniform approximation by double Fourier series
zbMATH Open document ID: 0704.42005
DOI: 10.1016/0021-9045(90)90021-H
published in: Journal of Approximation Theory
publication date: 1990-01-01T00:00:00Z
review text: The authors study the rate of strong uniform approximation of continuous functions f(x,y), \(2\pi\)-periodic in each variable, by the rectangular partial sums of their double Fourier series. They also obtain strong approximation rates to functions in the Lipschitz classes Lip(\(\alpha\),\(\beta\)) and Zygmund classes Z(\(\alpha\),\(\beta\)), where \(\alpha\), \(\beta\in (0,1]\). Also, the approximation rates of some conjugate functions are obtained. In almost all cases, these rates are shown to be the best possible.
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 4155130
zbMATH Keywords: rate of strong uniform approximation
zbMATH Keywords: Lipschitz classes
zbMATH Keywords: Zygmund classes
zbMATH Keywords: conjugate functions
author: Ferenc Móricz
author: Xianliang Shi
reviewed by: Ion Badea
MaRDI profile type: Publication
cites work: Q3897457
cites work: Über die Approximation im starken Sinne
cites work: Bemerkungen zur Approximation im starken Sinne
cites work: Strong and best approximation of Fourier series and the Lipschitz classes
cites work: Q3921635
cites work: Approximation to continuous functions by Cesàro means of double Fourier series and conjugate series
cites work: Q5564481
cites work: Q5827102
full work available at URL: 0021-9045(90)90021-h
OpenAlex ID: W2039024281
Recommended article: Q4463398
Recommended article: Strong approximation by Fourier series
Recommended article: Q3715586
Recommended article: Q3775976
Recommended article: On uniformly convergent double Fourier series
Recommended article: Q3351935
Recommended article: On almost universal double Fourier series
Recommended article: A note on strong approximation of Fourier series
Recommended article: Pointwise strong and very strong approximation of Fourier series
Recommended article: Q4852297
description: scientific article; zbMATH DE number 4155130