Geodesic
On rays of completely regular growth of an entire function
Sbornik. Mathematics, Tome 8 (1969) no. 4, pp. 437-450 
V. S. Azarin. On rays of completely regular growth of an entire function. Sbornik. Mathematics, Tome 8 (1969) no. 4, pp. 437-450. http://geodesic.mathdoc.fr/item/SM_1969_8_4_a0/
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     title = {On rays of completely regular growth of an~entire function},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper solves the problem of approximating a function, subharmonic in the entire plane, in a neighborhood of infinity by the logarithm of the modulus of an entire function. As an application of this result, we prove the existence of entire functions with an arbitrary closed set of rays of completely regular growth. Bibliography: 8 titles.

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

[2] M. Brelot, “Etude des fonctions sous-harmoniques au voisinage d'un point singulier”, Ann. Inst. Fourier, I (1949), 121–156 | MR

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

[4] W. K. Hayman, “Questions of regularity connected with the Phragment–Lindelof principle”, J. Math. Pures et Appl., 35:2 (1956), 115–126 | MR | Zbl

[5] V. S. Azarin, “Obobschenie odnoi teoremy Kheimana na subgarmonicheskie funktsii v $n$-mernom konuse”, Matem. sb., 66(108) (1965), 248–264 | MR | Zbl

[6] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, Fizmatgiz, M., 1966 | MR

[7] A. A. Goldberg, “Integral po poluadditivnoi mere i ego primenenie k teorii tselykh funktsii, IV”, Matem. sb., 66(108) (1965), 411–457 | MR

[8] I. I. Privalov, Subgarmonicheskie funktsii, Gostekhizdat, M., 1937