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Mat. Sb. (N.S.), 1987, Volume 132(174), Number 3, Pages 383–390 (Mi msb1871)  

This article is cited in 10 scientific papers (total in 11 papers)

On continuation of functions with polar singularities

A. S. Sadullaev, E. M. Chirka


Abstract: The main result is
Theorem 1 . If $f$ is a holomorphic function on the polydisk $'U\times U_n$ in $\mathbf C^n,$ and for each fixed $'a$ in some nonpluripolar set $E\subset 'U$ the function $f('a,z_n)$ can be continued holomorphically to the whole plane with the exception of some polar set of singularities, then $f$ can be continued holomorphically to $('U\times\mathbf C)\setminus S,$ where $S$ is a closed pluripolar subset of $'U\times\mathbf C$.
Some generalizations are also given, along with corollaries on extension of functions with analytic sets of singularities.
Bibliography: 13 titles.

Full text: PDF file (569 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1988, 60:2, 377–384

Bibliographic databases:

UDC: 517.55
MSC: Primary 32D15, 32C40; Secondary 30B40, 32D20, 32F05
Received: 02.12.1985

Citation: A. S. Sadullaev, E. M. Chirka, “On continuation of functions with polar singularities”, Mat. Sb. (N.S.), 132(174):3 (1987), 383–390; Math. USSR-Sb., 60:2 (1988), 377–384

Citation in format AMSBIB
\Bibitem{SadChi87}
\by A.~S.~Sadullaev, E.~M.~Chirka
\paper On continuation of~functions with polar singularities
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 132(174)
\issue 3
\pages 383--390
\mathnet{http://mi.mathnet.ru/msb1871}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=889599}
\zmath{https://zbmath.org/?q=an:0663.32009|0617.32018}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 2
\pages 377--384
\crossref{https://doi.org/10.1070/SM1988v060n02ABEH003175}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shirinbekov M., “On Hartog Theorem in Classes of Non-Analytical Functions”, 317, no. 4, 1991, 840–844  mathscinet  zmath  isi
    2. Shirinbekov M., “On Continuation Functions with Singularities”, Dokl. Akad. Nauk, 353:3 (1997), 310–312  mathnet  mathscinet  zmath  isi
    3. A. S. Sadullaev, “Pluriharmonic continuation in a fixed direction”, Sb. Math., 196:5 (2005), 765–775  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. A. Imomkulov, “On holomorphic continuation of functions defined on a pencil of boundary complex lines”, Izv. Math., 69:2 (2005), 345–363  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. 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  mathnet  crossref  mathscinet
    6. E. M. Chirka, “Variations of Hartogs' Theorem”, Proc. Steklov Inst. Math., 253 (2006), 212–220  mathnet  crossref  mathscinet  elib
    7. Marek Jarnicki, Peter Pflug, “A general cross theorem with singularities”, Analysis, 27:2-3 (2007), 181  crossref  mathscinet  zmath
    8. Azimbaj S. Sadullaev, “Some Problems in the Theory of Analytic Multifunctions”, Zhurn. SFU. Ser. Matem. i fiz., 1:4 (2008), 432–434  mathnet  elib
    9. A. S. Sadullaev, “On Analytic Multifunctions”, Math. Notes, 83:5 (2008), 652–656  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Sb. Math., 209:8 (2018), 1234–1247  mathnet  crossref  crossref  adsnasa  isi  elib
    11. A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1137–1144  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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