Approximation by rectangular partial sums of double conjugate Fourier series
type: Item
instance of: scholarly article
title: Approximation by rectangular partial sums of double conjugate Fourier series
zbMATH Open document ID: 0962.42006
published in: Journal of Approximation Theory
publication date: 2000-08-28T00:00:00Z
review text: The author examines the degree of approximation of the conjugate function \(\widehat f^{10}(x,y)\) by the symmetric rectangular partial sums of the series conjugate to double Fourier series in terms of oscillation of the function \[ \psi^{10}_{xy}(f, u,v)= f(x- u,y- v)- f(x+ u, y-v)+ f(x- u,y+ v)- f(x+ u,y+ v) \] over appropriate rectangles of the torus \(\mathbb{T}^2\), where \(f\in L^1(\mathbb{T}^2)\) is bounded. In particular, he obtains a conjugate version of the Dini-Lipschitz test on uniform convergence. He also obtains estimates in the case where the function \(f(x,y)\) is of bounded variation in the sense of Hardy and Krause.
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1423078
zbMATH Keywords: degree of approximation
zbMATH Keywords: conjugate function
zbMATH Keywords: double Fourier series
zbMATH Keywords: oscillation
zbMATH Keywords: Dini-Lipschitz test
author: Ferenc Móricz
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
full work available at URL: jath.1999.3422
OpenAlex ID: W2068033888
cites work: Q3897459
cites work: Q3736267
cites work: An estimate of the rate of convergence of the conjugate Fourier series of functions of bounded variation
cites work: A quantitative version of the Dirichlet-Jordan test for double Fourier series
cites work: A quantitative version of the Young test for the convergence of conjugate series
cites work: On the boundary values of functions of several complex variables, I
DOI: 10.1006/JATH.1999.3422
description: scientific article; zbMATH DE number 1423078