On~discrete weakly sufficient sets in certain spaces of entire functions
Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 349-357.

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

This article contains a study of weakly sufficient sets in a certain space of entire functions of exponential type. The following is a consequence of the results obtained: If $D$ is an infinite convex domain, then there exists a system $\{\lambda_k\}_{k=1}^\infty$ (which is minimal in a certain sense) such that any analytic function in $D$ can be represented by a series of the form $\sum a_k\exp\lambda_kz$. For bounded convex domains an analogous result was obtained previously by Leont'ev. Bibliography: 10 titles.
@article{IM2_1982_19_2_a7,
     author = {V. V. Napalkov},
     title = {On~discrete weakly sufficient sets in certain spaces of entire functions},
     journal = {Izvestiya. Mathematics },
     pages = {349--357},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a7/}
}
TY  - JOUR
AU  - V. V. Napalkov
TI  - On~discrete weakly sufficient sets in certain spaces of entire functions
JO  - Izvestiya. Mathematics 
PY  - 1982
SP  - 349
EP  - 357
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a7/
LA  - en
ID  - IM2_1982_19_2_a7
ER  - 
%0 Journal Article
%A V. V. Napalkov
%T On~discrete weakly sufficient sets in certain spaces of entire functions
%J Izvestiya. Mathematics 
%D 1982
%P 349-357
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a7/
%G en
%F IM2_1982_19_2_a7
V. V. Napalkov. On~discrete weakly sufficient sets in certain spaces of entire functions. Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 349-357. http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a7/

[1] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[2] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. I: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 88:1 (1972), 3–30

[3] Ehrenpreis L., Fourier Analysis in Several Complex Variables, N.Y., 1970 | MR

[4] Schneider D. M., “Sufficient sets for some spaces entire functions”, Trans. Amer. Math. Soc., 197 (1974), 161—180 | DOI | MR | Zbl

[5] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 326–355 | MR

[6] Napalkov V. V., “O diskretnykh dostatochnykh mnozhestvakh v nekotorykh prostranstvakh tselykh funktsii”, Dokl. AN SSSR, 250:4 (1980), 809–812 | MR | Zbl

[7] Krasichkov I. F., “Sravnenie tselykh funktsii konechnogo poryadka po raspredeleniyu ikh kornei”, Matem. sb., 70(112):2 (1966), 198–230 | Zbl

[8] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[9] Ehrenpreis L., “Analytically uniform spaces and some applications”, Trans. Amer. Math. Soc., 101 (1961), 52–74 | DOI | MR | Zbl

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