Geodesic
On the decomposition of an entire function of finite order into factors having given growth
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 225-226 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. S. Azarin. On the decomposition of an entire function of finite order into factors having given growth. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 225-226. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a5/

[1] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii. 1: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87 (129) (1972), 459–489

[2] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956

[3] V. S. Azarin, “O luchakh vpolne regulyarnogo rosta tseloi funktsii”, Matem. sb., 79 (121) (1969), 463–476 | MR | Zbl