Geodesic
Regular Growth of Various Characteristics of Entire Functions of Order Zero
Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 363-374.

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

We study the relationship between the strongly regular growth of an entire function $f$ of order zero, the existence of the angular density of its zeros, the behavior of the Fourier coefficients of the logarithm of $f$, and the regular growth of the logarithm of the modulus and the argument of $f$ in the $L^{p}[0,2\pi]$-metric, $p\ge1$.
Keywords: entire function, angular density, order of a function.
Mots-clés : Fourier coefficients 
@article{MZM_2016_100_3_a3,
     author = {N. V. Zabolotskii and O. V. Kostjuk},
     title = {Regular {Growth} of {Various} {Characteristics} of {Entire} {Functions} of {Order} {Zero}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {363--374},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a3/}
}
TY  - JOUR
AU  - N. V. Zabolotskii
AU  - O. V. Kostjuk
TI  - Regular Growth of Various Characteristics of Entire Functions of Order Zero
JO  - Matematičeskie zametki
PY  - 2016
SP  - 363
EP  - 374
VL  - 100
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a3/
LA  - ru
ID  - MZM_2016_100_3_a3
ER  - 
%0 Journal Article
%A N. V. Zabolotskii
%A O. V. Kostjuk
%T Regular Growth of Various Characteristics of Entire Functions of Order Zero
%J Matematičeskie zametki
%D 2016
%P 363-374
%V 100
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a3/
%G ru
%F MZM_2016_100_3_a3
N. V. Zabolotskii; O. V. Kostjuk. Regular Growth of Various Characteristics of Entire Functions of Order Zero. Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 363-374. http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a3/

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

[2] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956 | MR | Zbl

[3] V. S. Azarin, “O regulyarnosti rosta koeffitsientov Fure logarifma modulya tseloi funktsii”, Teor. funktsii, funkts. analiz i ikh prilozh., 27 (1977), 9–22 | MR | Zbl

[4] A. A. Kondratyuk, Ryady Fure i meromorfnye funktsii, Vischa shkola, Lvov, 1988 | Zbl

[5] A. A. Goldberg, N. V. Zabolotskii, “Indeks kontsentratsii subgarmonicheskoi funktsii nulevogo poryadka”, Matem. zametki, 34:2 (1983), 227–236 | MR | Zbl

[6] N. V. Zabolotskii, “Silno regulyarnyi rost tselykh funktsii nulevogo poryadka”, Matem. zametki, 63:2 (1998), 196–208 | DOI | MR | Zbl

[7] M. V. Zabolotskii, “An example of entire function of strongly regular growth”, Mat. Stud., 13:2 (2000), 145–148 | MR

[8] N. V. Zabolotskii, “Suschestvovanie uglovoi plotnosti kornei tselykh funktsii nulevogo poryadka”, Matem. zametki, 73:5 (2003), 698–703 | DOI | MR | Zbl

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

[10] O. Bodnar, M. Zabolotskii, “Rozpodil nuliv za argumentami ta koefitsienti Fur'e logarifmu tsiloï funktsiï”, Visn. Lviv. un-tu. Ser. mekh.-matem., 75 (2011), 17–27 | Zbl

[11] O. V. Bodnar, M. V. Zabolotskii, “Kriteriï regulyarnosti zrostannya logarifma modulya ta argumenta tsiloï funktsiï”, Ukr. matem. zhurn., 62:7 (2010), 885–893 | MR | Zbl

[12] R. Z. Kalinets, A. A. Kondratyuk, “Pro regulyarnist zrostannya modulya i argumenta tsiloï funktsiï v $L^p_{[0,2\pi]}$-metrits?”, Ukr. matem. zhurn., 50:7 (1998), 889–896 | MR | Zbl

[13] Ya. V. Vasilkiv, “Asimptotichna povedinka logarifmichnoï pokhidnoï ta logarifmiv meromorfnikh funktsii tsilkom regulyarnogo zrostannya v $\mathrm{L}^{p}[0,2\pi]$-metritsi. 1”, Mat. Stud., 12:1 (1999), 37–58 | MR

[14] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl

[15] A. V. Bratischev, “Ob obraschenii pravila Lopitalya”, Mekhanika sploshnoi sredy, Rostov-na-Donu, 1985, 28–42