Geodesic
On~conditions for the pluriharmonicity of the indicator of a~holomorphic function of several variables
Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 289-301

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider holomorphic functions $f(z,w)$ defined in a domain $E_r\times T_\alpha$, where $E_r=\{z:|z|$ and $T_\alpha=\{w:|\arg w|\alpha\}$; we obtain necessary and sufficient conditions for the pluriharmonicity of the indicator $$ h_f(z,w)=\varlimsup_{(z'w')\to(z,w)}\varlimsup_{t\to\infty}\frac{\ln|f(z',tw')|}{t^{\rho(t)}} $$ of $f(z,w)$ in $E_r\times T_\alpha$. We also obtain necessary and sufficient conditions for the pluriharmonicity of the indicator of a function $f(z)$ holomorphic in a cone. Bibliography: 6 titles. 
@article{SM_1975_27_2_a9,
     author = {P. Z. Agranovich and L. I. Ronkin},
     title = {On~conditions for the pluriharmonicity of the indicator of a~holomorphic function of several variables},
     journal = {Sbornik. Mathematics},
     pages = {289--301},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_27_2_a9/}
}
TY  - JOUR
AU  - P. Z. Agranovich
AU  - L. I. Ronkin
TI  - On~conditions for the pluriharmonicity of the indicator of a~holomorphic function of several variables
JO  - Sbornik. Mathematics
PY  - 1975
SP  - 289
EP  - 301
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1975_27_2_a9/
LA  - en
ID  - SM_1975_27_2_a9
ER  - 
%0 Journal Article
%A P. Z. Agranovich
%A L. I. Ronkin
%T On~conditions for the pluriharmonicity of the indicator of a~holomorphic function of several variables
%J Sbornik. Mathematics
%D 1975
%P 289-301
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1975_27_2_a9/
%G en
%F SM_1975_27_2_a9
P. Z. Agranovich; L. I. Ronkin. On~conditions for the pluriharmonicity of the indicator of a~holomorphic function of several variables. Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 289-301. http://geodesic.mathdoc.fr/item/SM_1975_27_2_a9/