Geodesic
Approximation of homogeneous subharmonic functions
Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 507-523 
R. S. Yulmukhametov. Approximation of homogeneous subharmonic functions. Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 507-523. http://geodesic.mathdoc.fr/item/SM_1989_62_2_a10/
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     author = {R. S. Yulmukhametov},
     title = {Approximation of homogeneous subharmonic functions},
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     volume = {62},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_2_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $u$ be a positive homogeneous subharmonic function, i.e. $$ u(tz)=tu(z),\qquad t>0,\quad z\in\mathbf C, $$ and let $\mu$ be its associated measure. Let the function $\rho(z)$ be such that $$ \mu(\{w\colon|w-z|<\rho(z)\})=1. $$ Then there exists an entire function $L$ for which \begin{gather*} |L(z)|\leqslant\exp u(z),\qquad z\in\mathbf C,\\ |L'(a)|\leqslant\exp(u(a)-\ln\rho(a)+O(\ln^\frac45\rho(a)\ln\ln\rho(a))),\qquad L(a)=0. \end{gather*} Bibliography: 6 titles.

[1] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[2] Leontev A. F., “Ryady eksponent dlya funktsii s zadannym rostom vblizi granitsy”, Izv. AN SSSR. Ser. matem., 44 (1980), 1308–1328 | MR

[3] Yulmukhametov R. S., “Dostatochnye mnozhestva v odnom prostranstve tselykh funktsii”, Matem. sb., 116(158) (1981), 425–439 | MR

[4] Yulmukhametov R. S., “Priblizhenie subgarmonicheskikh funktsii”, Matem. sb., 124(168) (1984), 393–415 | MR | Zbl

[5] Lyubarskii Yu. I., Sodin M. L., Analogi funktsii tipa sinusa dlya vypuklykh oblastei, Preprint No 17, FTINT, Kharkov, 1986

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