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Mat. Zametki, 1972, Volume 11, Issue 5, Pages 585–596 (Mi mz9826)  

Sufficient conditions for separation of analytic singularities in $C^n$ and a basis for a space of holomorphic functions

A. P. Yuzhakov

Institute of Physics, Siberian Branch, Academy of Sciences of the USSR

Abstract: It is proved that every holomorphic function of $n$ variables which has singularities on analytic surfaces, whose equations are linearly dependent, can be represented as the sum of functions, each of which has less than one singular surface. This fact is used to construct a basis for the space of functions which are holomorphic in the domain
$$ C^n\setminus\bigcup_{j=1}^Nż:\sum_{\nu=1}^n c_{j\nu}z_\nu+c_{j0}=0\}. $$


Full text: PDF file (1258 kB)

English version:
Mathematical Notes, 1972, 11:5, 356–361

Bibliographic databases:

UDC: 517.55
Received: 16.11.1970

Citation: A. P. Yuzhakov, “Sufficient conditions for separation of analytic singularities in $C^n$ and a basis for a space of holomorphic functions”, Mat. Zametki, 11:5 (1972), 585–596; Math. Notes, 11:5 (1972), 356–361

Citation in format AMSBIB
\Bibitem{Yuz72}
\by A.~P.~Yuzhakov
\paper Sufficient conditions for separation of analytic singularities in $C^n$ and a basis for a space of holomorphic functions
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 5
\pages 585--596
\mathnet{http://mi.mathnet.ru/mz9826}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=481069}
\zmath{https://zbmath.org/?q=an:0246.32011|0239.32009}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 5
\pages 356--361
\crossref{https://doi.org/10.1007/BF01158652}


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