Geodesic
Example of an entire function with given indicator and lower indicator
Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 541-558 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 $h_1(\varphi)$ 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. 
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V. S. Azarin. Example of an entire function with given indicator and lower indicator. Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 541-558. http://geodesic.mathdoc.fr/item/SM_1972_18_4_a0/

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

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

[3] M. Brelot, “Etude des fionctions sous-harmoiniques au voisinage d'un point singulier”, Ann. Inst. Fourier, 1 (1949), 121–156 | MR | Zbl

[4] V. S. Azarin, “O subgarmonicheskikh vo vsem prostranstve funktsiyakh vpolne regulyarnogo rosta”, Zap. Khark. un-ta i Khark. matem. ob-va, XXVIII (1961), 128–148 | MR

[5] A. A. Goldberg, I. V. Ostrovskii, “O proizvodnykh i pervoobraznykh tselykh funktsii vpolne regulyarnogo rosta”, Teoriya funktsii i funkts. analiz, 1972, no. 18, 185–201

[6] V. S. Azarin, “O regulyarnosti rosta tselykh funktsii”, DAN SSSR, 200:3 (1971), 511–512 | MR | Zbl