On dominating sets for uniform algebra on pseudoconvex domains
type: Item
instance of: scholarly article
title: On dominating sets for uniform algebra on pseudoconvex domains
zbMATH Open document ID: 1210.32014
author: So-Chin Chen
published in: Pure and Applied Mathematics Quarterly
publication date: 2011-01-03T00:00:00Z
review text: Let \(D\) be a bounded domain in \(\mathbb C^n\). Let \(A(D)\) be the uniform algebra on \(D\), i.e.\ the algebra of functions holomorphic in \(D\) and continuous up to the boundary, endowed with the supremum norm. A subset \(E\subset D\) is called a dominating set if for every two function \(f,g\in A(D)\) such that \(|f(z)|\leq|g(z)|\) for all \(z\in E\) then \(\|f\|_\infty\leq\|g\|_\infty\). The paper aims to show a relation between the notion of dominating set and that of Shilov boundary.
reviewed by: Alberto Saracco
Mathematics Subject Classification ID: 32T40
Mathematics Subject Classification ID: 32A38
zbMATH DE Number: 5831511
zbMATH Keywords: Shilov boundary
zbMATH Keywords: dominating sets
MaRDI profile type: Publication
full work available at URL: pamq.2010.v6.n3.a5
OpenAlex ID: W2317421516
DOI: 10.4310/PAMQ.2010.V6.N3.A5
Recommended article: Uniformization of strictly pseudoconvex domains. I
Recommended article: Uniformization of strictly pseudoconvex domains. II
Recommended article: On pseudoconvex domains in \(\mathbb{P}^n\)
Recommended article: Q3798959
Recommended article: Dominating sets for convex functions with some applications
Recommended article: Domination on sets and in \(H^p\)
Recommended article: Q3746090
Recommended article: Strictly pseudoconvex domains and algebraic varieties
Recommended article: Almost uniform domains and Poincar\'e inequalities
Recommended article: Q5687367
description: scientific article; zbMATH DE number 5831511