Geodesic
Approximation of subharmonic functions
Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 387-406 
R. S. Yulmukhametov. Approximation of subharmonic functions. Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 387-406. http://geodesic.mathdoc.fr/item/SM_1985_52_2_a5/
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     author = {R. S. Yulmukhametov},
     title = {Approximation of subharmonic functions},
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     volume = {52},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_2_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Given an arbitrary subharmonic function of finite order on the plane, an entire function $f(z)$ is constructed which satisfies the asymptotic relation $$ |u(z)-\ln|f(z)||\leqslant C\ln^2|z|,\qquad|z|\to\infty, $$ outside a sufficiently small exceptional set $E$. Functions with a logarithmic estimate are constructed in some special cases. Bibliography: 3 titles.

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

[2] Melnik Yu. I., “O predstavlenii regulyarnykh funktsii ryadami Dirikhle v zamknutom kruge”, Matem. sb., 97(139) (1975), 493–502 | MR | Zbl

[3] Yulmukhametov R. S., “Asimptoticheskaya approksimatsiya subgarmonicheskikh funktsii”, DAN SSSR, 264:4 (1982), 839–841 | MR | Zbl