The approximate identity kernels of product type for the Walsh system
type: Item
instance of: scholarly article
title: The approximate identity kernels of product type for the Walsh system
zbMATH Open document ID: 0619.42016
DOI: 10.1016/0021-9045(86)90019-5
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: At present there are only a few approximate identity kernels for the Walsh system such as the \(p^ N\)-truncated Dirichlet kernel, the Abel- Poisson kernel. In Chin. Ann. Math. Ser. A 4, 177-184 (1983; Zbl 0489.42025) \textit{W. Zheng} introduced a new kind of approximate identity kernels for the Walsh system, known as product type kernels. In this paper the author discusses the approximation properties of these product kernels. Estimates of their moments as well as a direct approximation theorem are obtained. In order to establish an inverse approximation theorem, the p-adic derivative of product type kernels are needed. The author estimates this derivative in \(L^ 1\)-norm.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 4004877
zbMATH Keywords: approximate identity kernels
zbMATH Keywords: Walsh system
zbMATH Keywords: Dirichlet kernel
zbMATH Keywords: Abel- Poisson kernel
author: Su Weiyi
reviewed by: Y. Sitaraman
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90019-5
OpenAlex ID: W2084479260
cites work: Q5621638
cites work: Walsh-fourier series and the concept of a derivative†
cites work: Q3315977
cites work: Q3704369
cites work: Q3882918
cites work: Q4740979
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description: scientific article; zbMATH DE number 4004877