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Mathematics of the USSR-Izvestiya, 1983, Volume 20, Issue 3, Pages 493–502
DOI: https://doi.org/10.1070/IM1983v020n03ABEH001612
(Mi im1625)
 

This article is cited in 22 scientific papers (total in 22 papers)

An estimate for polynomials on analytic sets

A. S. Sadullaev
References:
Abstract: Let $A$ be a connected, analytic (in general, not closed) subset of the complex space $\mathbf C^n$ and let $K\subset A$ be a compact set which is not pluri-polar in $A$. In this article it is proved that the extremal function $V(z,K)$ is locally bounded on $A$ if and only if $A$ belongs to some algebraic set of the same dimension as $A$. Moreover, it is shown that for an algebraic set $A$ in a neighborhood of any ordinary point $z^0\in A_0$ the function $V(z,K)$ can be represented as the limit of an increasing sequence of maximal functions.
Bibliography: 10 titles.
Received: 05.05.1980
Bibliographic databases:
UDC: 517.559
MSC: Primary 32F05; Secondary 32B15, 32J20
Language: English
Original paper language: Russian
Citation: A. S. Sadullaev, “An estimate for polynomials on analytic sets”, Math. USSR-Izv., 20:3 (1983), 493–502
Citation in format AMSBIB
\Bibitem{Sad82}
\by A.~S.~Sadullaev
\paper An estimate for polynomials on analytic sets
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 3
\pages 493--502
\mathnet{http://mi.mathnet.ru//eng/im1625}
\crossref{https://doi.org/10.1070/IM1983v020n03ABEH001612}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=661145}
\zmath{https://zbmath.org/?q=an:0582.32023|0511.32010}
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  • https://www.mathnet.ru/eng/im1625
  • https://doi.org/10.1070/IM1983v020n03ABEH001612
  • https://www.mathnet.ru/eng/im/v46/i3/p524
  • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:409
    Russian version PDF:168
    English version PDF:24
    References:66
    First page:1
     
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