Peak sets in pseudoconvex domains with isolated degeneracies
type: Item
instance of: scholarly article
title: Peak sets in pseudoconvex domains with isolated degeneracies
zbMATH Open document ID: 0547.32011
DOI: 10.1007/BF01161655
author: Andrei Iordan
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173558
review text: Let D be a bounded domain in \({\mathbb{C}}^ n\) with smooth boundary and \(A^{\infty}(D)\) the set of holomorphic functions in D which have a \(C^{\infty}\) extension to \(\bar D\). If D is strictly pseudoconvex, \textit{J.Chaumat} and \textit{A.-M. Chollet} proved that every compact subset of a peak set for \(A^{\infty}(D)\) is a peak set for \(A^{\infty}(D)\). The result was extended by \textit{A. V. Noell} to bounded pseudoconvex domains of finite type in \({\mathbb{C}}^ 2\). Here, we prove that the result is also true for bounded pseudoconvex domains in \({\mathbb{C}}^ n\) with smooth boundary, which are strictly pseudoconvex except at a finite number of points. The methods used in the paper are generalizations of those used by Chaumat and Chollet to prove the assertion in the strictly pseudoconvex case.
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32A40
zbMATH DE Number: 3871766
zbMATH Keywords: set of holomorphic functions
zbMATH Keywords: peak set
zbMATH Keywords: bounded pseudoconvex domains
MaRDI profile type: Publication
cites work: Caractérisation et propriétés des ensembles localement pics de \(A^\infty(D)\)
cites work: Holomorphic approximation and hyperfunction theory on a C\(^1\) totally real submanifold of a complex manifold
cites work: Peak sets in weakly pseudoconvex domains
cites work: Approximation by holomorphic functions on pseudoconvex domains with isolated degeneracies
OpenAlex ID: W2055770686
description: scientific article; zbMATH DE number 3871766