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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm3770https://doi.org/10.4213/mzm3770 https://www.mathnet.ru/eng/mzm/v83/i4/p545
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Abstract page: | 412 | Full-text PDF : | 168 | References: | 54 | First page: | 10 |
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