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This article is cited in 9 scientific papers (total in 9 papers)
On the decomposition of an entire function of finite order into factors having given growth
V. S. Azarin
Abstract:
In this paper the following result is proved:
Theorem. Let $\lambda_i,$ $i=1,\dots,n,$ be given such that $\lambda_i\geqslant0$ and $\sum\lambda_i=1$. Then any entire function $f(z)$ of finite order $\rho$ can be presented as a product of factors $f_i(z)$ such that
$$
\ln|f_i(z)|=\lambda_i\ln|f(z)|+o(|z|^\rho),\quad i=1,\dots,n,
$$
as $z\to\infty,$ $z$ outside a $C_0$-set.
Bibliography: 3 titles.
Received: 23.06.1972
Citation:
V. S. Azarin, “On the decomposition of an entire function of finite order into factors having given growth”, Math. USSR-Sb., 19:2 (1973), 225–226
Linking options:
https://www.mathnet.ru/eng/sm3008https://doi.org/10.1070/SM1973v019n02ABEH001747 https://www.mathnet.ru/eng/sm/v132/i2/p229
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