Example of an entire function with given indicator and lower indicator

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.
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