Discrete approximating operators on function algebras
type: Item
instance of: scholarly article
title: Discrete approximating operators on function algebras
zbMATH Open document ID: 0757.41028
DOI: 10.1007/BF01279026
author: Boris Shekhtman
published in: Constructive Approximation
publication date: 1992-09-27T00:00:00Z
review text: Let \(T\) be the unit circle and let \(A(T)\) be the disk algebra. For linear operators \(L_ n: A(T)\to A(T)\) of the form \(L_ n f=\sum_{k=1}^ n f(z_{n,k}\ell_{n,k}\), where \(z_{n,k}\in T\) and \(\ell_{n,k}\in A(T)\), \textit{G. Somorjai} [Constructive function theory, Proc. int. Conf., Blagoevgrad 1977, 489-496 (1980; Zbl 0396.41009)] proved that there exists a function \(f\in A(T)\) such that \(L_ nf\) does not converge to \(f\). The author gives a new presentation and various extensions of the cited theorem.
reviewed by: S.Aljančić
Mathematics Subject Classification ID: 41A45
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 61196
zbMATH Keywords: function algebras
zbMATH Keywords: discrete approximating operators
zbMATH Keywords: disk algebra
MaRDI profile type: Publication
cites work: MEASURES ORTHOGONAL TO POLYNOMIALS
cites work: A General Rudin-Carleson Theorem
cites work: Quasi-invariance and analyticity of measures on compact groups
cites work: Absolutely summing operators and translation invariant spaces of functions on compact abelian groups
cites work: The \(L_ p\) spaces
cites work: Analyticity, and the maximum modulus principle
cites work: Behavior of Polynomials of Best Uniform Approximation
Recommended article: Q5482549
Recommended article: Discrete approximation of integral operators
Recommended article: Approximation of continuous functions by certain discrete operators in Hölder's norms
Recommended article: Q3702405
Recommended article: Discrete approximation of unbounded operators and approximation of their spectra
Recommended article: Q4883512
Recommended article: Q5433813
Recommended article: On an approximation family of discrete polynomial operators
Recommended article: Discrete Sturm-Liouville operators and some problems of function theory
Recommended article: Approximation by pseudo-linear discrete operators
description: scientific article; zbMATH DE number 61196