On the convergence and saturation problem of a sequence of discrete linear operators of exponential type in \(L_ p(-\infty,\infty)\) spaces
type: Item
instance of: scholarly article
title: On the convergence and saturation problem of a sequence of discrete linear operators of exponential type in \(L_ p(-\infty,\infty)\) spaces
zbMATH Open document ID: 0614.41023
DOI: 10.1007/BF01956314
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The author considers the following discrete linear operators of entire exponential type: \[ I_{\sigma}(f,x)=\sum^{\infty}_{k=- \infty}f(t_ k)\quad \sin^ 2[\frac{\sigma}{2}(x-t_ k)]/[\frac{\sigma}{2}(x-t_ k)]^ 2 \] where k is an integer, \(\sigma t_ k=2k\pi\) and \(f\in L_ p(-\infty,\infty)\). Operators of this type were considered by \textit{P. Butzer} [Constructive function theory, Proc. int. Conf., Varna/Bulg. 1981, 258-274 (1983; Zbl 0542.94004)]. Different types of estimates for \[ \| I_{\sigma}(f)-f\|_ p\quad (1\leq p<\infty) \] are given and the saturation problem for this approximation problem is solved.
Mathematics Subject Classification ID: 41A40
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 3994197
zbMATH Keywords: discrete linear operators of entire exponential type
zbMATH Keywords: estimates
author: Dimiter P. Dryanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01956314
OpenAlex ID: W2085300826
description: scientific article; zbMATH DE number 3994197