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This article is cited in 4 scientific papers (total in 4 papers)
Approximation of homogeneous subharmonic functions
R. S. Yulmukhametov
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
Citation:
R. S. Yulmukhametov, “Approximation of homogeneous subharmonic functions”, Math. USSR-Sb., 62:2 (1989), 507–523
Linking options:
https://www.mathnet.ru/eng/sm3022https://doi.org/10.1070/SM1989v062n02ABEH003251 https://www.mathnet.ru/eng/sm/v176/i4/p511
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Abstract page: | 412 | Russian version PDF: | 120 | English version PDF: | 17 | References: | 69 |
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