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.
\Bibitem{Aza72}
\by V.~S.~Azarin
\paper Example of an entire function with given indicator and lower indicator
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 4
\pages 541--558
\mathnet{http://mi.mathnet.ru/eng/sm3246}
\crossref{https://doi.org/10.1070/SM1972v018n04ABEH001847}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=333174}
\zmath{https://zbmath.org/?q=an:0249.30023}
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https://doi.org/10.1070/SM1972v018n04ABEH001847
https://www.mathnet.ru/eng/sm/v131/i4/p541
This publication is cited in the following 4 articles:
G. G. Braichev, V. B. Sherstyukov, “Uniqueness Theorem for Entire Functions of Exponential Type”, Lobachevskii J Math, 45:6 (2024), 2672
G. G. Braichev, V. B. Sherstyukov, “Otsenki indikatorov tseloi funktsii s otritsatelnymi kornyami”, Vladikavk. matem. zhurn., 22:3 (2020), 30–46
V. B. Sherstyukov, “On a Problem of Leont'ev and Representing Systems of Exponentials”, Math. Notes, 74:2 (2003), 286–298
V. S. Azarin, “Indicators of an entire function and the regularity of the growth of the fourier coefficients of the logarithm of its modulus”, Funct. Anal. Appl., 9:1 (1975), 41–42
Citation in format AMSBIB
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