Approximation by Nörlund means of Walsh-Fourier series
type: Item
instance of: scholarly article
title: Approximation by Nörlund means of Walsh-Fourier series
zbMATH Open document ID: 0757.42009
DOI: 10.1016/0021-9045(92)90067-X
author: S. Singh
published in: Journal of Approximation Theory
publication date: 1993-01-16T00:00:00Z
review text: The authors prove under reasonable assumptions that the Nörlund kernel is quasi-positive. They use this to study the rate of approximation by Nörlund means for Walsh-Fourier series of a function in \(L^ p\) or \(\text{Lip}(\alpha,p)\) for \(\alpha>0\) and \(1\leq p\leq\infty\). These results generalize earlier work on Cesàro means by Yano, Jastrebova, and Skvortsov. This paper is very well written and contains two open problems near the end.
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 92498
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: Sidon type inequality
zbMATH Keywords: rate of approximation by Nörlund means for Walsh-Fourier series
zbMATH Keywords: Cesàro means
reviewed by: William R. Wade
MaRDI profile type: Publication
cites work: Q5585562
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cites work: Best approximation by Walsh polynomials
cites work: On Walsh-Fourier series
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full work available at URL: 0021-9045(92)90067-x
OpenAlex ID: W2038774678
description: scientific article; zbMATH DE number 92498