On estimating the rate of best trigonometric approximation by a modulus of smoothness
type: Item
instance of: scholarly article
title: On estimating the rate of best trigonometric approximation by a modulus of smoothness
zbMATH Open document ID: 1240.42004
published in: Acta Mathematica Hungarica
publication date: 2011-12-19T00:00:00Z
review text: The best trigonometric approximation in \(L_{p},1\leq p\leq \infty \), is characterized by a modulus of smoothness of order \(r\in N\), which is equivalent to zero if the function is a trigonometric polynomial of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses properties similar to those of the classical one. The Jackson-type estimate from the paper was established for the Hilbert space \(L_{2}\) by \textit{A. G. Babenko}, \textit{N. I. Chernykh} and \textit{V. T. Shevaldin} [Math.\ Notes 65, No. 6, 777-781 (1999; Zbl 0960.42001)]. Estimates for the best constant on the right side were also given, for \(p=\infty ,r=2,\) by \textit{V. T. Shevaldin} [Proceedings of the Steklov Institute of Mathematics 2001, Suppl. 1, S206--S213 (2001; Zbl 1117.41016)].
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 5990616
zbMATH Keywords: best trigonometric approximation
zbMATH Keywords: modulus of smoothness
zbMATH Keywords: \(K\)-functional, trigonometric B-spline
author: Borislav R. Draganov
author: Parvan E. Parvanov
reviewed by: W. Łenski
MaRDI profile type: Publication
full work available at URL: s10474-011-0072-8
OpenAlex ID: W2138852571
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DOI: 10.1007/S10474-011-0072-8
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description: scientific article; zbMATH DE number 5990616