Geodesic
On a Problem of Leont'ev and Representing Systems of Exponentials
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 301-313.

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

We study whether an entire function of exponential type has totally regular growth if its derivative increases sufficiently fast on the zero set of the function itself. In particular, for a function with a trigonometrically convex (or positive) lower indicator, we obtain a solution of a well-known problem of Leont'ev. As an application, we refine some already known results concerning the characterization of exponents of the representing systems of exponentials. 
@article{MZM_2003_74_2_a11,
     author = {V. B. Sherstyukov},
     title = {On a {Problem} of {Leont'ev} and {Representing} {Systems} of {Exponentials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--313},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a11/}
}
TY  - JOUR
AU  - V. B. Sherstyukov
TI  - On a Problem of Leont'ev and Representing Systems of Exponentials
JO  - Matematičeskie zametki
PY  - 2003
SP  - 301
EP  - 313
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a11/
LA  - ru
ID  - MZM_2003_74_2_a11
ER  - 
%0 Journal Article
%A V. B. Sherstyukov
%T On a Problem of Leont'ev and Representing Systems of Exponentials
%J Matematičeskie zametki
%D 2003
%P 301-313
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a11/
%G ru
%F MZM_2003_74_2_a11
V. B. Sherstyukov. On a Problem of Leont'ev and Representing Systems of Exponentials. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 301-313. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a11/

[1] Leontev A. F., “Ob usloviyakh razreshimosti analiticheskikh funktsii v ryady Dirikhle”, Izv. AN SSSR. Ser. matem., 36:6 (1972), 1282–1295 | MR | Zbl

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

[3] Bratischev A. V., “K odnoi zadache A. F. Leonteva”, Dokl. AN SSSR, 270:2 (1983), 265–267 | MR | Zbl

[4] Melnik Yu. I., “O predstavlenii regulyarnykh funktsii ryadami tipa ryadov Dirikhle”, Issledovanie po teorii priblizheniya funktsii i ikh prilozheniya, Kiev, 1978, 132–141 | MR | Zbl

[5] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, UMN, 36:1 (1981), 73–126 | MR | Zbl

[6] Bratischev A. V., Bazisy Kete, tselye funktsii i ikh prilozheniya, Diss. $\dots$ d.f.-m.n., Ekaterinburg, 1995

[7] Korobeinik Yu. F., “Maksimalnye i $\gamma$-dostatochnye mnozhestva. Prilozheniya k tselym funktsiyam, 2”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, 55, Kharkov, 1991, 23–34 | MR | Zbl

[8] Levin B. Ya., “Pochti periodicheskie funktsii s ogranichennym spektrom”, Aktualnye voprosy matematicheskogo analiza, Izd-vo RGU, Rostov-na-Donu, 1978, 112–124

[9] Azarin V. S., “Primer tseloi funktsii s zadannym indikatorom i nizhnim indikatorom”, Matem. sb., 89 (131):4 (1972), 541–557 | MR | Zbl

[10] Abanin A. V., “Geometricheskie kriterii predstavleniya analiticheskikh funktsii ryadami obobschennykh eksponent”, Dokl. RAN, 323:5 (1992), 807–810 | MR | Zbl

[11] Sherstyukov V. B., “K voprosu o $\gamma$-dostatochnykh mnozhestvakh”, Sib. matem. zh., 41:4 (2000), 935–943 | MR | Zbl

[12] Katsnelson V. E., “Ekvivalentnye normy v prostranstvakh tselykh funktsii”, Matem. sb., 92(134):1(9) (1973), 34–54 | MR | Zbl

[13] Logvinenko V. N., “Ob odnom mnogomernom obobschenii teoremy M. Kartrait”, Dokl. AN SSSR, 219:3 (1974), 546–549 | MR | Zbl