Peak sets in real-analytic convex boundaries
type: Item
instance of: scholarly article
title: Peak sets in real-analytic convex boundaries
zbMATH Open document ID: 0937.32009
author: Rachid Belhachemi
published in: Pacific Journal of Mathematics
publication date: 1999-09-26T00:00:00Z
review text: For a domain \(D\Subset\mathbb{C}^n\) with smooth boundary, \(A^\infty (D)\) denotes the space of holomorphic in \(D\) and \({\mathcal C}^\infty\) on \(D\). The main result of the paper is the following. Theorem. Let \(D\Subset \mathbb{C}^n\) be a convex domain with real analytic boundary. Assume \(K\) is a peak set for \(A^\infty(D)\), and \(L\) is a compact subset of \(K\). Then \(L\) is a peak set for \(A^\infty (D)\). Recall that a closed subset \(K\subset \partial D\) is a peak set for \(A^\infty(D)\) if there exists a function \(f\in A^\infty (D)\) so that \(f\equiv 1\) on \(K\) and \(|f|<1\) on \(\overline D\setminus K\).
Mathematics Subject Classification ID: 32E35
zbMATH DE Number: 1344268
zbMATH Keywords: holomorphic function
zbMATH Keywords: peak set
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
full work available at URL: pjm.1998.185.209
OpenAlex ID: W1988663920
DOI: 10.2140/PJM.1998.185.209
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description: scientific article; zbMATH DE number 1344268