On the maximum modulus principle for polynomials in a quasidisk
type: Item
instance of: scholarly article
title: On the maximum modulus principle for polynomials in a quasidisk
zbMATH Open document ID: 1099.30010
DOI: 10.1007/BF02787832
published in: Journal d'Analyse Mathématique
publication date: 2006-03-09T00:00:00Z
review text: Main result: Let \(K\) be a compact subset of a bounded quasidisk \(G\subset \mathbb C\). Let \(p_n\) be a polynomial of degree \(\leq n\) such that \(m\,:=\,\inf_{z\in G}| p_n(z)| \,<\,\sup_{z\in G}| p_n(z)| \). Then \(\| p_n\| _K\,\leq\, (1-\alpha_n)\| p_n\| _G\), where \(\alpha_n \,=\,\alpha_n(G,K,m)\) depends on \(G,\,k\,,\,m\) and on the geometrical structure of \(\partial G\).
Mathematics Subject Classification ID: 30C80
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 5010211
zbMATH Keywords: polynomial
zbMATH Keywords: quasidisk
zbMATH Keywords: maximum modulus principle
author: V. V. Andrievskii
reviewed by: Józef Siciak
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02787832
OpenAlex ID: W2051618651
description: scientific article; zbMATH DE number 5010211