Minimal dimension families of complex lines sufficient for holomorphic extension of functions
type: Item
instance of: scholarly article
title: Minimal dimension families of complex lines sufficient for holomorphic extension of functions
zbMATH Open document ID: 1235.32008
DOI: 10.1134/S0037446611020091
author: S. G. Myslivets
author: A. M. Kytmanov
author: V. I. Kuzovatov
published in: Siberian Mathematical Journal
publication date: 2011-06-24T00:00:00Z
review text: Let \(\mathcal L_\Gamma\) be a family of complex lines in \(\mathbb C^n\) that pass through a given complex manifold \(\Gamma\) in a given direction \(b\). Let \(D\) be a bounded simply connected domain with connected boundary of class \(\mathcal C^2\) whose closure does not intersect \(\Gamma\). Then a function \(f\in \mathcal C(\partial D)\) is said to enjoy the one-dimensional extension property if \(f\) restricted to any \(l\in\mathcal L_\Gamma\) extends holomorphically to \(l\cap D\). The authors study the existence of holomorphic extensions of functions with one-dimensional extension property using the technique of Bochner-Martinelli integrals.
reviewed by: Gerd Schmalz
Mathematics Subject Classification ID: 32D99
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 5912833
zbMATH Keywords: holomorphic extension
zbMATH Keywords: Bochner-Martinelli integral
zbMATH Keywords: harmonic function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5912833