Geodesic
Theorems of Paley–Wiener and Müntz–Szász type
Izvestiya. Mathematics, Tome 11 (1977) no. 4, pp. 821-847 
M. M. Dzhrbashyan; V. M. Martirosyan. Theorems of Paley–Wiener and Müntz–Szász type. Izvestiya. Mathematics, Tome 11 (1977) no. 4, pp. 821-847. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a6/
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     title = {Theorems of {Paley{\textendash}Wiener} and {M\"untz{\textendash}Sz\'asz} type},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper a new integral representation of the well-known function classes $\mathscr H_2[\alpha]$ ($0\alpha1$) is established, which in the limiting case $\alpha=1$ goes into the Paley–Wiener theorem. A Hilbert space metric is introduced into the classes $\mathscr H_2[\alpha]$ ($0\alpha+\infty$), and a criterion for closedness of certain systems of functions in these spaces is established. In particular, a theorem of Müntz–Szász type in the complex domain is proved, and a complete intrinsic description is given of the corresponding nonclosed systems. Bibliography: 9 titles.

[1] Viner N., Peli R., Preobrazovanie Fure v kompleksnoi oblasti, Nauka, M., 1964 | MR

[2] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[3] O. Szasz, “Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen”, Math. Ann., 77 (1916), 482–496 | DOI | MR | Zbl

[4] M. M. Dzhrbashyan, “O popolnenii i zamykanii sistemy $\{e^{-\mu_{k^x}}x^{s_{k^{-1}}}\}_1^\infty$”, Dokl. AN SSSR, 141:3 (1961), 539–542 | Zbl

[5] Dzhrbashyan M. M., Avetisyan A. E., “Integralnye predstavleniya nekotorykh klassov funktsii, analiticheskikh v oblasti ugla”, Dokl. AN SSSR, 120:3 (1958), 457–460 ; РЎРёР±. матРμРј. Р¶., 1:3 (1960), 383–426 | MR | Zbl | MR | Zbl

[6] “Dzhrbashyan M. M.”, Dokl. AN SSSR, 219:6 (1974), 1302–1305 | MR | Zbl

[7] Akopyan S. A., Khachatryan I. O., “O zamykanii sistem funktsii tipa Mittag-Lefflera”, Izv. AN SSSR. Ser. matem., 40 (1976), 96–114 | Zbl

[8] Martirosyan V. M., “O dvukh prostranstvakh analiticheskikh v poluploskosti funktsii”, Izv. AN Arm. SSR. Ser. matem., X:2 (1975), 182–185

[9] Dzhrbashyan M. M., Martirosyan V. M., “Teoremy tipa Vinera–Peli i Myuntsa–Sasa”, Dokl. AN SSSR, 225:5 (1975), 1001–1004 | MR | Zbl