Geodesic
Growth of entire functions of two complex variables that are slowly increasing in one of the variables
Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 63-92.

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

This article studies the asymptotic properties of one general class of entire functions of two complex variables. The class consists of those functions which from the point of view of growth and value distribution theory are the natural generalization of $p$-dimensional entire curves. For functions in this class the concepts of defect and deviation are defined, sharp bounds for these quantities are deduced, and it is shown that the set of all positive deviations is an exceptional set. Corresponding quantities are introduced and some of their properties are described for functions of $n$ ($n>2$) complex variables. Bibliography: 26 titles. 
@article{IM2_1976_10_1_a4,
     author = {V. P. Petrenko},
     title = {Growth of entire functions of two complex variables that are slowly increasing in one of the variables},
     journal = {Izvestiya. Mathematics },
     pages = {63--92},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a4/}
}
TY  - JOUR
AU  - V. P. Petrenko
TI  - Growth of entire functions of two complex variables that are slowly increasing in one of the variables
JO  - Izvestiya. Mathematics 
PY  - 1976
SP  - 63
EP  - 92
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a4/
LA  - en
ID  - IM2_1976_10_1_a4
ER  - 
%0 Journal Article
%A V. P. Petrenko
%T Growth of entire functions of two complex variables that are slowly increasing in one of the variables
%J Izvestiya. Mathematics 
%D 1976
%P 63-92
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a4/
%G en
%F IM2_1976_10_1_a4
V. P. Petrenko. Growth of entire functions of two complex variables that are slowly increasing in one of the variables. Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 63-92. http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a4/

[1] Weyl H., Meromorphic functions and analytic curves, Princeton, 1943 | MR

[2] Ahlfors L., “The theory of meromorphic curves”, Acta Soc. Sci. Fenn., III:4 (1941), 1–31 | MR

[3] Cartan H., “Sur les zéros des combinaisons linèaires de $p$ fonctions holomorphes donnée”, Mathematica, 7 (1933), 5–33

[4] Goldberg A. A., “Nekotorye voprosy teorii raspredeleniya znachenii”, dopolnenie k knige: G. Vittikh, Noveishie issledovaniya po odnoznachnym analiticheskim funktsiyam, Fizmatgiz, M., 1960 | MR

[5] Petrenko V. P., “O velichinakh otklonenii tselykh krivykh nizhnego poryadka $\lambda1$”, Dokl. AN SSSR, 207:3 (1972), 538–540 | MR | Zbl

[6] Petrenko V. P., Khussain M., “O roste tselykh krivykh”, Izv. AN SSSR. Ser. matem., 37 (1973), 466–477 | MR | Zbl

[7] Khussain M., “O defektakh i velichinakh otklonenii tselykh krivykh”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 20, Kharkov, 1974, 173–184

[8] Petrenko V. P., “Rost $Q$-psevdomeromorfnykh funktsii”, Sib. matem. zhurnal, 15:1 (1974), 76–89 | MR | Zbl

[9] Fuks B. A., Vvedenie v teoriyu analiticheskikh funktsii mnogikh kompleksnykh peremennykh, Fizmatgiz, M., 1962 | MR

[10] Lamzina T. B., “O roste meromorfnykh funktsii i tselykh krivykh”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 18, Kharkov, 1973, 202–215 | MR | Zbl

[11] Lamzina T. B., “O velichinakh otklonenii tselykh krivykh nizhnego poryadka $\lambda1$”, Izv. AN SSSR. Ser. matem., 38:2 (1974), 323–332 | MR | Zbl

[12] Petrenko V. P., “O roste tselykh krivykh”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 20, Kharkov, 1974, 134–142 | MR

[13] Paley R. E. C., “A note on integral function”, Proc. Cambridge Philos. Soc., 28 (1932), 262–265 | DOI | Zbl

[14] Nevanlinna R., Odnoznachnye analiticheskie funktsii, Gostekhizdat, M., L., 1941

[15] Kheiman U. K., Meromorfnye funktsii, Mir, M., 1966 | MR

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

[17] Petrenko V. P., “Rost meromorfnykh funktsii konechnogo nizhnego poryadka”, Izv. AN SSSR. Ser. matem., 33 (1969), 414–456 | MR

[18] Petrenko V. P., “Izuchenie struktury mnozhestva polozhitelnykh otklonenii meromorfnykh funktsii. II”, Izv. AN SSSR. Ser. matem., 34 (1970), 32–56 | MR

[19] Petrenko V. P., “Velichiny otklonenii meromorfnykh funktsii nizhnego poryadka menshe edinitsy”, Dokl. AN SSSR, 187:1 (1969), 40–42 | MR | Zbl

[20] Goldberg A. A., “O roste tseloi funktsii po luchu”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 1, Kharkov, 1965, 45–74

[21] Petrenko V. P., “Nekotorye otsenki logarifmicheskoi proizvodnoi meromorfnoi funktsii”, Izv. AN ArmSSR, 17:1 (1964), 23–27 | MR

[22] Goldberg A. A., Ostrovskii I. V., Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR

[23] Petrenko V. P., “Izuchenie struktury mnozhestva polozhitelnykh otklonenii meromorfnykh funktsii. I”, Izv. AN SSSR. Ser. matem., 33 (1969), 1330–1348 | MR

[24] Petrenko V. P., “Rost kvazikonformnykh tselykh krivykh”, Dokl. AN SSSR, 216:5 (1974), 982–985 | MR | Zbl

[25] Govorov N. V., “O probleme Peili”, Funktsionalnyi analiz i ego prilozheniya, 3:2 (1969), 35–40 | MR

[26] Dahlberg B., “Mean values of subharmonic functions”, Ark. Mat., 10:2 (1972), 293–309 | DOI | MR | Zbl