On the Completeness of a System of Analytic Functions
Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 163-177.

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

A new method of establishing the completeness of systems of analytic functions in the space $A(D)$ is considered. We indicate some applications of the results obtained to the case of the principle of doubly symmetric Kazmin sets, to the Abel–Goncharov problem (the uniqueness and construction problem), and to some other cases.
Keywords: analytic function, completeness of systems of analytic functions, doubly symmetric Kazmin set, Riemann boundary-value problem.
Mots-clés : Liouville's theorem
@article{MZM_2011_89_2_a0,
     author = {G. I. Andriyanov},
     title = {On the {Completeness} of a {System} of {Analytic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--177},
     publisher = {mathdoc},
     volume = {89},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a0/}
}
TY  - JOUR
AU  - G. I. Andriyanov
TI  - On the Completeness of a System of Analytic Functions
JO  - Matematičeskie zametki
PY  - 2011
SP  - 163
EP  - 177
VL  - 89
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a0/
LA  - ru
ID  - MZM_2011_89_2_a0
ER  - 
%0 Journal Article
%A G. I. Andriyanov
%T On the Completeness of a System of Analytic Functions
%J Matematičeskie zametki
%D 2011
%P 163-177
%V 89
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a0/
%G ru
%F MZM_2011_89_2_a0
G. I. Andriyanov. On the Completeness of a System of Analytic Functions. Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 163-177. http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a0/

[1] Yu. A. Kazmin, “Obschaya problema momentov v kompleksnoi oblasti”, Proceedings of the Conference on the Constructive Theory of Functions (Approximation Theory) (Budapest, 1969), Akadémiai Kiadó, Budapest, 1972, 225–254 | MR | Zbl

[2] A. A. Mirolyubov, “K voprosu o polnote sistemy pokazatelnykh funktsii”, Sib. matem. zhurn., 8:1 (1967), 3–10 | Zbl

[3] Yu. A. Kazmin, “Polnota v krivolineinoi polose posledovatelnosti pokazatelnykh funktsii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1968, no. 6, 18–30 | MR | Zbl

[4] R. P. Boas, jr., “A completeness theorem”, Amer. J. Math., 62:1 (1940), 312–318 | DOI | MR | Zbl

[5] R. P. Boas, jr., “Some uniqueness theorems for entire functions”, Amer. J. Math., 62:1 (1940), 319–324 | DOI | MR | Zbl

[6] G. I. Andriyanov, “Modifitsirovannaya problema momentov v kompleksnoi oblasti”, Matem. zametki, 72:6 (2002), 804–814 | MR | Zbl

[7] M. A. Evgrafov, Osnovnye ponyatiya interpolyatsii tselykh funktsii, Preprint IPM AN SSSR, M., 1975

[8] Yu. A. Kazmin, “Ob odnoi zadache Gelfonda–Ibragimova. I”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1965, no. 3, 28–36 | MR | Zbl

[9] Yu. A. Kazmin, “Ob odnom geometricheskom priznake polnoty”, Matem. sb., 100:2 (1976), 181–190 | MR | Zbl

[10] Yu. A. Kazmin, “O printsipe dvazhdy simmetrichnykh mnozhestv v teorii interpolyatsii”, Vsesoyuznyi simpozium po teorii approksimatsii funktsii v kompleksnoi oblasti, Tezisy dokladov, Ufa, 1980

[11] S. Ya. Alper, “O polnote sistemy analiticheskikh funktsii”, Dokl. AN SSSR, 206:6 (1949), 1029–1032 | MR | Zbl

[12] I. I. Ibragimov, I. S. Arshon, “O polnote nekotorykh sistem analiticheskikh funktsii funktsii”, Dokl. AN SSSR, 197:5 (1971), 1010–1013 | MR | Zbl

[13] M. A. Evgrafov, Analiticheskie funktsii, Nauka, M., 1991 | MR | Zbl

[14] G. I. Andriyanov, Interpolyatsionnaya zadacha Abelya–Goncharova, Diss. $\dots$ kand. fiz.- matem. nauk, M., 1998

[15] F. D. Gakhov, Kraevye zadachi, Nauka, M., 1977 | MR | Zbl

[16] I. I. Ibragimov, Metody interpolyatsii i nekotorye ikh primeneniya, Nauka, M., 1971 | MR | Zbl

[17] V. L. Goncharov, “Interpolyatsionnye protsessy i tselye funktsii”, UMN, 1937, no. 3, 113–143

[18] A. O. Gelfond, “Problema predstavleniya i edinstvennosti tseloi analiticheskoi funktsii pervogo poryadka”, UMN, 1937, no. 3, 144–174

[19] A. O. Gelfond, Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR | Zbl

[20] R. V. Adibekyan, “Ob interpolyatsionnoi zadache Abelya–Goncharova dlya tselykh funktsii eksponentsialnogo tipa”, Uch. zap. Erevansk. gos. un-ta. Ser. estestv. nauki, 3 (1983), 20–27 | MR | Zbl