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Mathematics of the USSR-Sbornik, 1986, Volume 53, Issue 1, Pages 271–281
DOI: https://doi.org/10.1070/SM1986v053n01ABEH002920
(Mi sm2082)
 

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

A criterion for rapid rational approximation in $\mathbf C^n$

A. S. Sadullaev
References:
Abstract: This article gives a necessary and sufficient condition for a function which is holomorphic in a neighborhood of zero to belong to the class $R^0$. This criterion, which is formulated in terms of the Taylor coefficients of the function, is then applied to give a description of the singular set of holomorphic functions of several variables which admit rapid rational approximation relative to Lebesgue measure (i.e., which belongs to the class $R^0$). In particular,
Theorem. If $\mathscr O(D)\subset R^0$, then the complement $\mathbf C^n\setminus\widehat D$ of the envelope of holomorphy $D$ is a pluripolar set.
This theorem together with a well-known result of A. A. Gonchar gives a complete description of the domains for which $\mathscr O(D)\subset R^0$: this property is satisfied if and only if $\mathbf C^n\setminus\widehat D$ is a pluripolar set.
Bibliography: 11 titles.
Received: 13.10.1983
Bibliographic databases:
UDC: 517.55
MSC: Primary 32E30; Secondary 31B15
Language: English
Original paper language: Russian
Citation: A. S. Sadullaev, “A criterion for rapid rational approximation in $\mathbf C^n$”, Math. USSR-Sb., 53:1 (1986), 271–281
Citation in format AMSBIB
\Bibitem{Sad84}
\by A.~S.~Sadullaev
\paper A~criterion for rapid rational approximation in~$\mathbf C^n$
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 1
\pages 271--281
\mathnet{http://mi.mathnet.ru//eng/sm2082}
\crossref{https://doi.org/10.1070/SM1986v053n01ABEH002920}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=764481}
\zmath{https://zbmath.org/?q=an:0592.32013}
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  • https://doi.org/10.1070/SM1986v053n01ABEH002920
  • https://www.mathnet.ru/eng/sm/v167/i2/p269
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:425
    Russian version PDF:132
    English version PDF:23
    References:65
     
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