Sur la frontière de Shilov des domaines de \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Sur la frontière de Shilov des domaines de \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0573.32017
DOI: 10.1007/BF01455917
author: Nessim Sibony
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164041
review text: Given \(n\geq 1\), we construct a circled bounded domain \(\Omega\) in \({\mathbb{C}}^ n\) such that (i) \({\bar \Omega}\) is polynomially convex, (ii) the Shilov boundary of \({\bar \Omega}\) with respect to the algebra P(\({\bar \Omega}\)) is of Hausdorff dimension 1. This answers a question of \textit{A. G. Vituškin} [cf. Sov. Math., Dokl. 14(1973), 1618-1619 (1974); translation from Dokl. Math. Nauk SSSR 213, 14-15 (1973; Zbl 0292.32011)].
Mathematics Subject Classification ID: 32E20
Mathematics Subject Classification ID: 32A38
zbMATH DE Number: 3914706
zbMATH Keywords: polynomially convex
zbMATH Keywords: Shilov boundary
MaRDI profile type: Publication
cites work: Polynomial Approximation and Hulls in Sets in Finite Linear Measure in C n
cites work: Q5583306
cites work: On Some Extremal Functions and their Applications in the Theory of Analytic Functions of Several Complex Variables
cites work: Q4163454
cites work: Q4046376
cites work: Q4043344
cites work: Q4104417
description: scientific article; zbMATH DE number 3914706