Geodesic
Approximation of subharmonic functions
Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 387-406

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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. 
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     author = {R. S. Yulmukhametov},
     title = {Approximation of subharmonic functions},
     journal = {Sbornik. Mathematics},
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     volume = {52},
     number = {2},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_2_a5/}
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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/