This article is cited in 4 papers

Example of an entire function with given indicator and lower indicator

V. S. Azarin


Abstract: In this paper, the following result is proved.
Theorem. Let $h_1(\varphi)$ and $h_2(\varphi)$ be two $\rho$-trigonometrically convex functions. There is an entire function $f(z)$ of finite order $\rho$ such that its indicator $h_f(\varphi)=\max[h_1(\varphi),h_2(\varphi)]$ and its lower indicator $\underline h_f(\varphi)=\min[h_1(\varphi),h_2(\varphi)]$.
Applications of this theorem are given.
Bibliography: 6 titles.

UDC: 517.535.4

MSC: 30A64

Received: 07.02.1972

 English version: Mathematics of the USSR-Sbornik, 1972, 18:4, 541–558

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