Geodesic
Sharp Estimates of Types of Entire Functions with Zeros on Rays
Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 503-515 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The least values of types of entire functions with zeros of prescribed upper and lower densities located on the rays in the complex plane are obtained.
Keywords: entire function with zeros on rays, type of an entire function, upper (lower) $\rho$-density of the sequence of zeros of an entire function, Levin–Pfluger theory of entire functions. 
@article{MZM_2015_97_4_a2,
     author = {G. G. Braichev},
     title = {Sharp {Estimates} of {Types} of {Entire} {Functions} with {Zeros} on {Rays}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {503--515},
     year = {2015},
     volume = {97},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a2/}
}
TY  - JOUR
AU  - G. G. Braichev
TI  - Sharp Estimates of Types of Entire Functions with Zeros on Rays
JO  - Matematičeskie zametki
PY  - 2015
SP  - 503
EP  - 515
VL  - 97
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a2/
LA  - ru
ID  - MZM_2015_97_4_a2
ER  - 
%0 Journal Article
%A G. G. Braichev
%T Sharp Estimates of Types of Entire Functions with Zeros on Rays
%J Matematičeskie zametki
%D 2015
%P 503-515
%V 97
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a2/
%G ru
%F MZM_2015_97_4_a2
G. G. Braichev. Sharp Estimates of Types of Entire Functions with Zeros on Rays. Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 503-515. http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a2/

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

[2] A. Pfluger, “Die Wertverteilung und das Verhalten von Betrag und Argument einer speziellen Klasse analytischer Funktionen. I”, Comment. Math. Helv., 11:1 (1938), 180–214 | DOI | MR | Zbl

[3] A. Pfluger, “Die Wertverteilung und das Verhalten von Betrag und Argument einer speziellen Klasse analytischer Funktionen. II”, Comment. Math. Helv., 12 (1939), 25–65 | DOI | MR | Zbl

[4] A. A. Goldberg, “Integral po poluadditivnoi mere i ego prilozhenie k teorii tselykh funktsii. I”, Matem. sb., 58:3 (1962), 289–334 | MR | Zbl

[5] A. A. Goldberg, “Integral po poluadditivnoi mere i ego prilozhenie k teorii tselykh funktsii. II”, Matem. sb., 61:3 (1963), 334–349 | MR | Zbl

[6] A. A. Goldberg, “Integral po poluadditivnoi mere i ego prilozhenie k teorii tselykh funktsii. III”, Matem. sb., 65:3 (1964), 414–453 | MR | Zbl

[7] A. A. Goldberg, “Integral po poluadditivnoi mere i ego prilozhenie k teorii tselykh funktsii. IV”, Matem. sb., 66:3 (1965), 411–457 | MR | Zbl

[8] A. Yu. Popov, “Naimenshii vozmozhnyi tip pri poryadke $\rho1$ kanonicheskikh proizvedenii s polozhitelnymi nulyami zadannoi verkhnei $\rho$-plotnosti”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2005, no. 1, 31–36 | MR | Zbl

[9] A. Yu. Popov, “O naimenshem tipe tseloi funktsii poryadka $\rho$ s kornyami zadannoi verkhnei $\rho$-plotnosti, lezhaschimi na odnom luche”, Matem. zametki, 85:2 (2009), 246–260 | DOI | MR | Zbl

[10] A. Yu. Popov, “Razvitie teoremy Valirona–Levina o naimenshem vozmozhnom tipe tseloi funktsii s zadannoi verkhnei $\rho$-plotnostyu kornei”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 49, RUDN, M., 2013, 132–164

[11] G. Valiron, “Sur les fonctions entières d'ordre nul et d'ordre fini et en particulier les fonctions à correspondance régulière”, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. (3), 5 (1913), 117–257 | DOI | MR

[12] A. E. Avetisyan, “O tselykh funktsiyakh poryadka $\rho$ ($1\rho2$)”, Izv. AN Arm. SSR. Matem., 23:6 (1988), 557–574 | MR | Zbl

[13] B. N. Khabibullin, “Posledovatelnost nulei golomorfnykh funktsii, predstavlenie meromorfnykh funktsii. II. Tselye funktsii”, Matem. sb., 200:2 (2009), 129–158 | DOI | MR | Zbl

[14] G. G. Braichev, V. B. Sherstyukov, “O naimenshem vozmozhnom tipe tselykh funktsii poryadka $\rho\in(0,1)$ s polozhitelnymi nulyami”, Izv. RAN. Ser. matem., 75:1 (2011), 3–28 | DOI | MR | Zbl

[15] G. G. Braichev, O. V. Sherstyukova, “Naibolshii vozmozhnyi nizhnii tip tseloi funktsii poryadka $\rho\in(0;1)$ s nulyami fiksirovannykh $\rho$-plotnostei”, Matem. zametki, 90:2 (2011), 199–215 | DOI | MR | Zbl

[16] V. B. Sherstyukov, “Minimalnoe znachenie tipa tseloi funktsii poryadka menshe edinitsy s nulyami zadannykh plotnostei, lezhaschimi v ugle”, Materialy 17 mezhdunarodnoi Saratovskoi zimnei shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya” (27 yanvarya – 3 fevralya 2014 g.), Izd-vo Saratovskogo un-ta, Saratov, 2014, 309–310

[17] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular Variation, Encyclopedia Math. Appl., 27, Cambridge University Press, Cambridge, 1987 | MR | Zbl

[18] R. Ph. Boas, jr., Entire Functions, Pure Appl. Math., 5, Academic Press, New York, 1954 | MR | Zbl

[19] R. M. Redheffer, “On even entire functions with zeros having a density”, Trans. Amer. Math. Soc., 77 (1954), 32–61 | DOI | MR | Zbl