Exponential series in Smirnov spaces and interpolation by entire functions of special classes

Yu. I. Lyubarskii

Izvestiya. Mathematics, Tome 32 (1989) no. 3, pp. 563-586

Résumé

This paper studies problems of the Dirichlet series expansions of elements of Smirnov spaces in convex domains, and related theorems on interpolation by entire functions of exponential type. Bibliography: 22 titles.

Bibliographie

[1] Leontev A. F., “O predstavlenii proizvolnykh funktsii ryadami Dirikhle”, Dokl. AN SSSR, 164:1 (1965), 40–42 | MR

[2] Leontev A. F., Ryady eksponent, Nauka, M., 1976, 536 | MR

[3] Leontev A. F., “O predstavlenii analiticheskikh funktsii v mnogougolnoi zamknutoi oblasti ryadami Dirikhle”, Izv. AN SSSR. Ser. matem., 38:1 (1974), 127–137 | MR

[4] Dzyadyk V. K., “Ob usloviyakh skhodimosti ryadov Dirikhle na zamknutykh mnogougolnikakh”, Matem. sb., 95(137):4(12) (1974), 475–493

[5] Levin B. Ya., Lyubarskii Yu. I., “Interpolyatsiya tselymi funktsiyami spetsialnykh klassov i svyazannye s neyu razlozheniya v ryady eksponent”, Izv. AN SSSR. Ser. matem., 39:3 (1975), 657–702 | MR | Zbl

[6] Sedletskii A. M., “O razlozhenii funktsii v ryady Dirikhle na zamknutykh vypuklykh mnogougolnikakh”, Sibirskii matem. zhurn., XIX:4 (1978), 878–887

[7] Melnik Yu. I., “O predstavlenii funktsii ryadami Dirikhle v zamknutom kruge”, Matem. sb., 97:4 (1975), 493–502 | MR

[8] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L^2(-\pi,\pi)$”, Uch. zap. matem. otd. Kharkovskogo un-ta i Kharkovskogo matem. ob-va. Ser. 4, XXVII, 1961, 39–48

[9] Levin B. Ya., “Interpolyatsiya tselymi funktsiyami eksponentsialnogo tipa”, Matem. fizika i funktsion. analiz. Sb. nauchn. tr. FTINT AN USSR, 1, Kharkov, 1969, 136–146 | MR

[10] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhteorizdat, M., L., 1950, 338

[11] Kotelnikov V. A., “O propusknoi sposobnosti “efira” i provoloki v elektrosvyazi”, Materialy k 1-mu Vsesoyuznomu s'ezdu po voprosam svyazi i razvitiya slabotochnoi promyshlennosti, Upravlenie svyazi RKK, M., 1933

[12] Lyubarskii Yu. I., Sodin M. L., Analogi funktsii tipa sinusa dlya vypuklykh oblastei, Preprint No 17, Fiziko-tekhnicheskogo in-t nizkikh temperatur AN USSR, Kharkov, 1986, 42

[13] Mazya V. G., Prostranstva S. L. Soboleva, LGU, L., 1986, 415 | MR

[14] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973, 342 | MR

[15] S. G. Krein (red.), Funktsionalnyi analiz, Nauka, M., 1972, 544 | MR | Zbl

[16] Dzhrbashyan M. M., “O kanonicheskom predstavlenii meromorfnykh v kruge funktsii”, Dokl. AN ArmSSR, 1945, no. 3, 3–9 | MR

[17] Dzhrbashyan M. M., “K probleme predstavimosti analiticheskikh funktsii”, Soobsch. in-ta matem. i mekh. AN ArmSSR, 2 (1945), 3–40

[18] Belinskii Ya. P., Obschie svoistva kvazikonformnykh otobrazhenii, Nauka, Novosibirsk, 1974, 98 | MR | Zbl

[19] Coifman R. R., Fefferman C., “Weighted norm inequalities for maximal functions and singular integrals”, Stud. Math. (RPL), LI:3 (1974), 241–250 | MR

[20] Lyubarskii Yu. I., “Teorema Vinera–Peli dlya vypuklykh mnozhestv”, Izv. AN ArmSSR. Matematika, 23 (1988) | MR | Zbl

[21] Lyubarskii Yu. I., “Teorema Vinera–Peli dlya vypuklykh mnozhestv”, Dokl. AN USSR. Ser. A, 1986, no. 3, 14 | MR | Zbl

[22] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhteorizdat, M., 1956, 632