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Tr. Mat. Inst. Steklova, 2006, Volume 253, Pages 158–174 (Mi tm91)  

This article is cited in 1 scientific paper (total in 1 paper)

Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections

A. S. Sadullaev, S. A. Imomkulov

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan

Abstract: The paper is of survey character. We present and discuss recent results concerning the extension of functions that admit holomorphic or plurisubharmonic extension in a fixed direction. These results are closely related to Hartogs' fundamental theorem, which states that if a function $f(z)$, $z = (z_1,z_2,…,z_n)$, is holomorphic in a domain $D\subset \mathbb C^n$ in each variable $z_j$, then it is holomorphic in $D$ in the $n$-variable sense.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 144–159

Bibliographic databases:

UDC: 517.533+517.576
Received in September 2005

Citation: A. S. Sadullaev, S. A. Imomkulov, “Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections”, Complex analysis and applications, Collected papers, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 158–174; Proc. Steklov Inst. Math., 253 (2006), 144–159

Citation in format AMSBIB
\Bibitem{SadImo06}
\by A.~S.~Sadullaev, S.~A.~Imomkulov
\paper Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections
\inbook Complex analysis and applications
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2006
\vol 253
\pages 158--174
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm91}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338695}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 144--159
\crossref{https://doi.org/10.1134/S0081543806020131}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748333106}


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    This publication is cited in the following articles:
    1. A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Sb. Math., 209:8 (2018), 1234–1247  mathnet  crossref  crossref  adsnasa  isi  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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