Abstract:
In this paper it is proved that a function of n complex variables that is meromorphic in each variable separately on a special set X is globally meromorphic in the neighborhood of X. This result is an analog of a theorem of J. Siciak on separate holomorphicity.
Bibliography: 8 titles.
\Bibitem{Kaz76}
\by M.~V.~Kazaryan
\paper On functions of several complex variables that are separately meromorphic
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 4
\pages 481--489
\mathnet{http://mi.mathnet.ru/eng/sm2772}
\crossref{https://doi.org/10.1070/SM1976v028n04ABEH001664}
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\zmath{https://zbmath.org/?q=an:0351.32003}
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Linking options:
https://www.mathnet.ru/eng/sm2772
https://doi.org/10.1070/SM1976v028n04ABEH001664
https://www.mathnet.ru/eng/sm/v141/i4/p538
This publication is cited in the following 5 articles:
A. S. Sadullaev, S. A. Imomkulov, “Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections”, Proc. Steklov Inst. Math., 253 (2006), 144–159
Bernard Shiffman, Aspects of Mathematics, E 26, Contributions to Complex Analysis and Analytic Geometry / Analyse Complexe et Géométrie Analytique, 1994, 243
Shiffman B., “Complete Characterization of Holomorphic-Chains of Codimension One”, Math. Ann., 274:2 (1986), 233–256
M. V. Kazaryan, “Meromorphic extension with respect to groups of variables”, Math. USSR-Sb., 53:2 (1986), 385–398
M. Shirinbekov, “On Hartogs compacts of holomorphy”, Math. USSR-Sb., 43:3 (1982), 403–411
Citation in format AMSBIB
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