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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 107–121 (Mi ufa137)

On some families of complex lines sufficient for holomorphic extension of functions

V. I. Kuzovatov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: The present article is based on the result related to the holomorphic extension of functions. Functions with the one-dimensional holomorphic extension property along families of complex lines are discussed. Real analytic functions given on the boundary of a bounded domain $D$ in $\mathbb C^n$, $n>1$ with the one-dimensional holomorphic extension property along families of complex lines are considered. The existence of holomorphic extensions of these functions to $D$ is studied depending on the kind of the domain and location of the families of complex lines.

Keywords: real analytic function, holomorphic extension, functions with the one-dimensional holomorphic extension property.

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UDC: 517.55

Citation: V. I. Kuzovatov, “On some families of complex lines sufficient for holomorphic extension of functions”, Ufimsk. Mat. Zh., 4:1 (2012), 107–121

Citation in format AMSBIB
\Bibitem{Kuz12} \by V.~I.~Kuzovatov \paper On some families of complex lines sufficient for holomorphic extension of functions \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 1 \pages 107--121 \mathnet{http://mi.mathnet.ru/ufa137} 

• http://mi.mathnet.ru/eng/ufa137
• http://mi.mathnet.ru/eng/ufa/v4/i1/p107

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