On some representing systems in spaces of analytic functions

Yu. F. Korobeinik

Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 487-509.

Résumé

Let $E_\rho(z)$ be the Mittag-Leffler function. This article investigates the connection between “representing” properties for systems $\mathscr E_{\rho,\Lambda}=\{E_{\rho}(\lambda_kz)\}^{\infty}_{k=1}$ and $\mathscr E^{(n)}_{\rho,\Lambda}=\{E_\rho(\lambda_kz),zE_\rho(\lambda_kz),\dots,z^nE_\rho(\lambda_kz)\}^{\infty}_{k=1}$, $n\geqslant1$, as well as for systems $\mathscr E^1_{\rho,\Lambda}=\{E_\rho(\lambda_{k,1}z)\}^\infty_{k=1}$, $\mathscr E^2_{\rho,\Lambda}=\{E_\rho(\lambda_{k,2}z)\}^\infty_{k=1}$, and $\mathscr E^3_{\rho,\Lambda}=\mathscr E^1_{\rho,\Lambda}\cup\mathscr E^2_{\rho,\Lambda}$ in spaces of analytic functions. Bibliography: 18 titles.

Bibliographie

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

[2] Melnik Yu. I., “K voprosu o predstavlenii regulyarnykh funktsii ryadami Dirikhle”, Matem. zametki, 21:5 (1977), 641–651 | MR | Zbl

[3] Korobeinik Yu. F., “Predstavlyayuschie sistemy eksponent i netrivialnye razlozheniya nulya”, DAN SSSR, 252:3 (1980), 528–531 | MR | Zbl

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

[5] Korobeinik Yu. F., “Ob odnoi dvoistvennoi svyazi. I: Obschie rezultaty. Prilozheniya k prostranstvam Freshe”, Matem. sborn., 97(139):2 (1975), 193–229 | MR | Zbl

[6] Korobeinik Yu. F., “Ob odnoi dvoistvennoi svyazi”, Matem. analiz i ego prilozheniya, no. 7, Rostov-na-Donu, 1975, 200–208 | Zbl

[7] Epifanov O. V., Lenev A. A., “O razreshimosti odnogo integralnogo uravneniya v prostranstve analiticheskikh funktsii”, Matematicheskii analiz i ego prilozheniya, no. 6, Rostov-na-Donu, 1974, 258–261 | Zbl

[8] Leontev A. F., Obobscheniya ryadov eksponent, Nauka, M., 1981 | MR

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

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

[11] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 325–355 | MR | Zbl

[12] Abanin A. V., Nekotorye predstavlyayuschie sistemy v $\rho$-vypuklykh oblastyakh, Depon. v VINITI 16.VII.1979, No 2571-79, RZhmat, 1979, 10 B 197 dep., Rostovskii un-t, Rostov-na-Donu, 1979

[13] Dragilev M. M., Zakharyuta V. P., Korobeinik Yu. F., “Dvoistvennaya svyaz mezhdu nekotorymi voprosami teorii bazisa i interpolyatsii”, DAN SSSR, 215:3 (1974), 522–525 | MR | Zbl

[14] Bratischev A. V., “O razreshimosti interpolyatsionnoi zadachi v prostranstvakh $[\rho(r), H(\theta))$ i $[\rho(r), H(\theta)]$”, Mekhanika sploshnoi sredy, Rostovskii un-t, Rostov-na-Donu, 1981, 49–53

[15] Korobeinik Yu. F., “Ob analiticheskikh resheniyakh integralnogo uravneniya s yadrom, zavisyaschim ot raznosti argumentov”, Matematicheskii analiz i ego prilozheniya, no. 3, Rostov-na-Donu, 1971, 3–19 | MR | Zbl

[16] Korobeinik Yu. F., Leontev A. F., “O svoistve vnutr-prodolzhaemosti predstavlyayuschikh sistem eksponent”, Matem. zametki, 28:2 (1980), 243–254 | MR | Zbl

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

[18] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR