Pseudoconvex domains with peak functions at each point of the boundary
type: Item
instance of: scholarly article
title: Pseudoconvex domains with peak functions at each point of the boundary
zbMATH Open document ID: 0619.32012
author: Andrei Iordan
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let D be a bounded pseudoconvex domain in \({\mathbb{C}}^ n\) with \(C^{\infty}\) boundary and let \(A^{\infty}(D)\) be the algebra of holomorphic functions in D which have a \(C^{\infty}\) extension to \=D. If D is strictly pseudoconvex, it is a very known result of H. Rossi that each point of the boundary is a peak point for \(A^{\infty}(D)\). This happens also if D is weakly pseudoconvex and the weakly pseudoconvex boundary points are of strict type. In this paper, there are given other conditions on the set of weakly pseudoconvex boundary points of a pseudoconvex domain in \({\mathbb{C}}^ n\), which ensure that each point of the boundary is a peak point for \(A^{\infty}(D)\).
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 4004605
zbMATH Keywords: algebra of holomorphic functions
zbMATH Keywords: weakly pseudoconvex boundary points
zbMATH Keywords: pseudoconvex domain
zbMATH Keywords: peak point
MaRDI profile type: Publication
full work available at URL: pjm.1988.133.277
OpenAlex ID: W2083465225
DOI: 10.2140/PJM.1988.133.277
description: scientific article; zbMATH DE number 4004605