2018
Том 70
№ 9

On the Growth of the Maximum of the Modulus of an Entire Function on a Sequence

Filevych P. V.

Abstract

Let M f(r) and μf(r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let Φ be a continuously differentiable function convex on (−∞, +∞) and such that x = o(Φ(x)) as x → +∞. We establish that, in order that the equality $\lim \inf \limits_{r \to + \infty} \frac{\ln M_f (r)}{\Phi (\ln r)} = \lim \inf \limits_{r \to + \infty} \frac{\ln \mu_f (r)}{\Phi (\ln r)}$ be true for any entire function f, it is necessary and sufficient that ln Φ′(x) = o(Φ(x)) as x → +∞.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 8, pp 1386-1392.

Citation Example: Filevych P. V. On the Growth of the Maximum of the Modulus of an Entire Function on a Sequence // Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1149-1153.

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