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Mathematics of the USSR-Sbornik, 1989, Volume 62, Issue 2, Pages 507–523
DOI: https://doi.org/10.1070/SM1989v062n02ABEH003251
(Mi sm3022)
 

This article is cited in 4 scientific papers (total in 4 papers)

Approximation of homogeneous subharmonic functions

R. S. Yulmukhametov
References:
Abstract: Let $u$ be a positive homogeneous subharmonic function, i.e.
$$ u(tz)=tu(z),\qquad t>0,\quad z\in\mathbf C, $$
and let $\mu$ be its associated measure. Let the function $\rho(z)$ be such that
$$ \mu(\{w\colon|w-z|<\rho(z)\})=1. $$
Then there exists an entire function $L$ for which
\begin{gather*} |L(z)|\leqslant\exp u(z),\qquad z\in\mathbf C,\\ |L'(a)|\leqslant\exp(u(a)-\ln\rho(a)+O(\ln^\frac45\rho(a)\ln\ln\rho(a))),\qquad L(a)=0. \end{gather*}

Bibliography: 6 titles.
Received: 18.03.1987
Bibliographic databases:
UDC: 517.5
MSC: Primary 31A05, 30D15, 41A30; Secondary 30B50
Language: English
Original paper language: Russian
Citation: R. S. Yulmukhametov, “Approximation of homogeneous subharmonic functions”, Math. USSR-Sb., 62:2 (1989), 507–523
Citation in format AMSBIB
\Bibitem{Yul87}
\by R.~S.~Yulmukhametov
\paper Approximation of homogeneous subharmonic functions
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 507--523
\mathnet{http://mi.mathnet.ru/eng/sm3022}
\crossref{https://doi.org/10.1070/SM1989v062n02ABEH003251}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=933700}
\zmath{https://zbmath.org/?q=an:0665.31002}
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  • https://doi.org/10.1070/SM1989v062n02ABEH003251
  • https://www.mathnet.ru/eng/sm/v176/i4/p511
  • This publication is cited in the following 4 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:412
    Russian version PDF:120
    English version PDF:17
    References:69
     
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