Boundary analogues of Hartog's theorem
type: Item
instance of: scholarly article
title: Boundary analogues of Hartog's theorem
zbMATH Open document ID: 0732.32006
DOI: 10.1007/BF00970171
published in: Siberian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: Let \(\Omega\) be a bounded domain in \({\mathbb{C}}^ n\). A family L of complex lines is called ``sufficient'' if from: (i) \(f\in C(\delta \Omega),\) (ii) for every \(\ell \in L\), \(f| \ell \cap \delta \Omega\) has an analytic prolongation in \(\ell \cap {\bar \Omega},\) it follows that f is analytic in \(\Omega\) and continuous in \({\bar \Omega}\). The aim of this paper is to give examples of ``sufficient'' families of complex lines.
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32E35
zbMATH DE Number: 4210526
zbMATH Keywords: Hartog's theorem
zbMATH Keywords: analytic prolongation
zbMATH Keywords: complex lines
author: Mark L. Agranovsky
author: Alexander M. Semenov
reviewed by: I. Mihuţ
MaRDI profile type: Publication
cites work: The boundary values of holomorphic functions of several complex variables
cites work: Q3958740
cites work: On holomorphic extensions from spheres in ℂ2
cites work: Q3767608
cites work: Q3869608
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description: scientific article; zbMATH DE number 4210526