Weighted uniform polynomial approximation and moduli of smoothness on continua in the complex plane
type: Item
instance of: scholarly article
title: Weighted uniform polynomial approximation and moduli of smoothness on continua in the complex plane
zbMATH Open document ID: 1253.41005
published in: Journal of Approximation Theory
publication date: 2012-03-22T00:00:00Z
review text: The starting point of the analysis is a result due to \textit{G. Mastroianni} and \textit{V. Totik} [J. Approx. Theory 110, No. 2, 180--199 (2001; Zbl 0981.41016)]. The aim of the paper is to extend this result to the case of weighted polynomial approximation on compact sets in the complex plane. The main results of the paper are contained in Theorem 1 and Theorem 2, where the extension to the complex plane is characterized.
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 6017048
zbMATH Keywords: polynomial approximation
zbMATH Keywords: conformal mapping
zbMATH Keywords: constructive description
zbMATH Keywords: continuous function
author: V. V. Andrievskii
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: j.jat.2011.10.009
OpenAlex ID: W1970507389
cites work: Q5512337
cites work: Geometric properties of V. K. Dzyadyk's regions
cites work: Description of classes of functions with given rate of decrease of their best uniform polynomial approximations
cites work: THE GEOMETRIC STRUCTURE OF REGIONS, AND DIRECT THEOREMS OF THE CONSTRUCTIVE THEORY OF FUNCTIONS
cites work: Q4206974
cites work: Constructive theory of analytic functions on a quasidisk
cites work: Conformal invariants in constructive theory of functions of complex variable. Transl. from the Russian by D. N. Kravchuk
cites work: On \(L^p\)-discrepancy of signed measures
cites work: CONFORMAL MAPPINGS AND THE APPROXIMATION OF ANALYTIC FUNCTIONS IN DOMAINS WITH A QUASICONFORMAL BOUNDARY
cites work: Q3817079
cites work: Q4126820
cites work: Q4139002
cites work: Q3961322
cites work: Q3237285
cites work: On the theory of approximation of functions on closed sets of the complex plane (with reference to a problem of S. M. Nikol'skii)
cites work: Q5569283
cites work: Q3752617
cites work: Q5685358
cites work: Best approximation and moduli of smoothness for doubling weights
cites work: Q5835448
cites work: Q4000499
cites work: Constructive characterization of classes of continuous functions of a set \(\mathfrak M\subset\mathbb{C}\) for the \(k-th\) modulus of continuity
cites work: Q5607484
cites work: Q4120973
cites work: Q5803437
cites work: Constructive characteristic of continuous functions defined on smooth arcs
DOI: 10.1016/J.JAT.2011.10.009
Recommended article: Weighted Polynomial Approximation of Entire Functions on Unbounded Subsets of the Complex Plane
Recommended article: Q4851232
Recommended article: Polynomial approximation with varying weights on compact sets of the complex plane
Recommended article: Q3356840
Recommended article: Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
Recommended article: Q3124097
Recommended article: Q5116797
Recommended article: Q4365442
Recommended article: Weighted polynomial approximation, quasianalyticity and analytic continuation.
Recommended article: Weighted polynomial approximation in the complex plane
description: scientific article; zbMATH DE number 6017048