A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables
Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 238-258.

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

We present results on the relationship between the growth of the maximum modulus and the decay of Taylor coefficients of entire functions of several variables. The results are obtained by two different methods, the first of which had been proposed earlier by Oskolkov for the one-dimensional case, and the second is based on the use of the Legendre–Jung–Fenchel conjugates of the weight functions. Attention is mainly paid to the characterization of the growth of entire functions with respect to the conjunction of variables; however, some results are obtained for the case in which there is different growth with respect to different variables.
@article{MZM_1997_62_2_a7,
     author = {Yu. F. Korobeinik},
     title = {A relationship between the maximum modulus and {Taylor} coefficients of entire functions of several complex variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {238--258},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a7/}
}
TY  - JOUR
AU  - Yu. F. Korobeinik
TI  - A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables
JO  - Matematičeskie zametki
PY  - 1997
SP  - 238
EP  - 258
VL  - 62
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a7/
LA  - ru
ID  - MZM_1997_62_2_a7
ER  - 
%0 Journal Article
%A Yu. F. Korobeinik
%T A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables
%J Matematičeskie zametki
%D 1997
%P 238-258
%V 62
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a7/
%G ru
%F MZM_1997_62_2_a7
Yu. F. Korobeinik. A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 238-258. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a7/

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

[2] Oskolkov V. A., “O nekotorykh voprosakh teorii tselykh funktsii”, Matem. sb., 184:1 (1993), 129–148 | Zbl

[3] Oskolkov V. A., Svoistva funktsii, zadannykh znacheniyami ikh lineinykh funktsionalov, Diss. ... k. f.-m. n., MGU, M., 1995

[4] Ronkin L. I., Elementy teorii analiticheskikh funktsii mnogikh peremennykh, Naukova dumka, Kiev, 1977 | Zbl

[5] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 | Zbl

[6] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | Zbl

[7] Bratischev A. V., Korobeinik Yu. F., “O nekotorykh kharakteristikakh rosta subgarmonicheskikh funktsii”, Matem. sb., 106:1 (1978), 44–65 | MR | Zbl

[8] Rokafellar R., Vypuklyi analiz, Mir, M., 1973