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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 545–551
DOI: https://doi.org/10.4213/mzm3770
(Mi mzm3770)
 

This article is cited in 26 scientific papers (total in 26 papers)

On Families of Complex Lines Sufficient for Holomorphic Extension

A. M. Kytmanov, S. G. Myslivets

Krasnoyarsk State University
References:
Abstract: It is shown that the set $\mathfrak L_\Gamma$ of all complex lines passing through a germ of a generating manifold $\Gamma$ is sufficient for any continuous function $f$ defined on the boundary of a bounded domain $D\subset\mathbb C^n$ with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from $\mathfrak L_\Gamma$ to admit a holomorphic extension to $D$ as a function of many complex variables.
Keywords: holomorphic extension property, family of complex lines, Hartogs' theorem, Bochner–Martinelli integral, Sard's theorem, Cauchy–Riemann condition.
Received: 03.07.2006
Revised: 26.03.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 500–505
DOI: https://doi.org/10.1134/S0001434608030231
Bibliographic databases:
UDC: 517.55
Language: Russian
Citation: A. M. Kytmanov, S. G. Myslivets, “On Families of Complex Lines Sufficient for Holomorphic Extension”, Mat. Zametki, 83:4 (2008), 545–551; Math. Notes, 83:4 (2008), 500–505
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm3770
  • https://doi.org/10.4213/mzm3770
  • https://www.mathnet.ru/eng/mzm/v83/i4/p545
  • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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