Geodesic
On a problem of A. O. Gel'fond
Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 509-530 
Yu. A. Kaz'min. On a problem of A. O. Gel'fond. Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 509-530. http://geodesic.mathdoc.fr/item/SM_1973_19_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A complete solution is found of the interpolation problem for constructing entire functions $g(z)$ given their values on a geometric progression $$ g(\beta^n)=b_n,\qquad n=0,1,2,\dots, $$ where $\beta$ is a complex number, $|\beta|>1$. Bibliography: 12 titles.

[1] A. O. Gelfond, Ischislenie konechnykh raznostei, Gostekhizdat, Moskva, 1952

[2] A. O. Gelfond, “O funktsiyakh, tselochislennykh v tochkakh geometricheskoi progressii”, Matem. sb., 40 (1933), 42–47 | Zbl

[3] Yu. A. Kazmin, “Problema momentov v kompleksnoi oblasti”, Vestnik MGU, seriya matem. mekh., 1967, no. 1, 3–11 | MR

[4] Yu. A. Kazmin, “Ob odnoi obschei zadache iz teorii interpolyatsii”, DAN SSSR, 194:6 (1970), 1251–1254 | MR

[5] Yu. A. Kazmin, “Obschaya problema momentov v kompleksnoi oblasti”, Proc. Conf. on the Constructive Theory of Functions, Budapest, 1972, 225–254 | MR

[6] Yu. A. Kazmin, “K probleme momentov v kompleksnoi oblasti”, DAN SSSR, 204:6 (1972), 1309–1312 | MR

[7] Yu. A. Kazmin, “Obschaya problema momentov. Teoremy edinstvennosti”, DAN SSSR, 205:1 (1972), 19–22 | MR

[8] F. D. Gakhov, Kraevye zadachi, Fizmatgiz, Moskva, 1963

[9] S. Banakh, Kurs funktsionalnogo analiza, Kiev, 1948

[10] Yu. A. Kazmin, “O bazisakh iz posledovatelnykh primitivnykh”, Matem. zametki, 3:3 (1968), 237–246 | MR

[11] M. G. Khaplanov, “Matrichnyi priznak bazisa v prostranstve analiticheskikh funktsii”, DAN SSSR, 80:2 (1951), 177–180; M. G. Khaplanov, Lineinye operatory v analiticheskom prostranstve i ikh prilozheniya, Dissertatsiya, Rostov-na-Donu, 1960

[12] S. Ya. Alper, “O polnote sistemy analiticheskikh funktsii”, DAN SSSR, 66:6 (1949), 1029–1032 | MR