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Математическая физика, анализ, геометрия, 2002, том 9, номер 3, страницы 509–520
(Mi jmag314)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Approximation of subharmonic functions of slow growth
Igor Chyzhykov Department of Mechanics and Mathematics, Ivan Franko National University, 1 University Str., Lviv, 79000, Ukraine
Аннотация:
Let $u$ be a subharmonic function in $\mathbb C$, $\mu_u$ its Riesz measure. Suppose that $C_1\le\mu(\{z:R<|z|\le R\psi(R)\}\le C_2$ $(R\ge R_1)$ for some positive constants $C_1$, $C_2$, and $R_1$, and a slowly growing to $+\infty$ function $\psi(r)$ such that $r/\psi(r) \nearrow +\infty$ ($r\to+\infty$). Then there exist an entire function $f$, constants $K_1=K_1(C_1,C_2)$, $K_2=K_2(C_2)$ and a set $E\subset\mathbb C$ such that
$$
|u(z)-\log|f(z)||\le K_1\log\psi(|z|), \qquad z\to\infty, \quad z\notin E,
$$
and $E$ can be covered by the system of discs $D_{z_k}(\rho_k)$ satisfying
$$
\sum_{R<|z_k|<R\psi(R)}\frac{\rho_k\psi(|z_k|)}{|z_k|}<K_2,
$$
as $R_2\to+\infty$. We prove also that the estimate of the exceptional set is sharp up to a constant factor.
Поступила в редакцию: 30.11.2001
Образец цитирования:
Igor Chyzhykov, “Approximation of subharmonic functions of slow growth”, Матем. физ., анал., геом., 9:3 (2002), 509–520
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag314 https://www.mathnet.ru/rus/jmag/v9/i3/p509
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Страница аннотации: | 159 | PDF полного текста: | 50 |
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