Envelopes of holomorphy and polynomial hulls
type: Item
instance of: scholarly article
title: Envelopes of holomorphy and polynomial hulls
zbMATH Open document ID: 0686.32010
DOI: 10.1007/BF01449212
author: John Wermer
author: Herbert J. Alexander
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164397
review text: This paper continues the study of polynomial hulls by the authors. Let Y be a compact subset of \({\mathbb{C}}^ 2\) contained in \(\partial \Delta \times \Delta\), where \(\Delta\) is the open unit disk in the plane such that for \(\lambda\in \partial \Delta\) the complement of \(Y_{\lambda}:=\{w:\) (\(\lambda\),w)\(\in Y\}\) is connected. The polynomial hull of Y is denoted by \(\hat Y.\) For a certain class \({\mathcal F}\) of bounded and holomorphic functions on \(\Omega_ 0:=\Delta \times ({\mathbb{C}}\setminus \Delta)\), Theorem 1 proves the existence of holomorphic extensions to \(\Omega^*:=(\Delta \times {\mathbb{C}})\setminus \hat Y\). Theorem 2 says that if \(Y_{\lambda}\) is convex for \(\lambda\in \partial \Delta\), then the extensions of particular functions in \({\mathcal F}\) have no zeros on \(\Omega^*\).
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32E20
zbMATH DE Number: 4124082
zbMATH Keywords: envelopes of holomorphy
zbMATH Keywords: holomorphic extension
zbMATH Keywords: polynomial hulls
MaRDI profile type: Publication
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OpenAlex ID: W2053380920
description: scientific article; zbMATH DE number 4124082