Laplace transforms of functionals on Bergman spaces
Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 3-41.

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

A complete description is given of the dual of the Bergman space on a plane bounded convex domain.
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K. P. Isaev; R. S. Yulmukhametov. Laplace transforms of functionals on Bergman spaces. Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 3-41. http://geodesic.mathdoc.fr/item/IM2_2004_68_1_a1/

[1] Gaier D., Lektsii po teorii approksimatsii v kompleksnoi ploskosti, Mir, M., 1986 | MR | Zbl

[2] Lutsenko V. I., Yulmukhametov R. S., “Teorema Peli–Vinera v prostranstvakh Smirnova”, Tr. MIAN, 200, Nauka, M., 1991, 245–254 | MR | Zbl

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

[4] Likht M. K., “Zamechanie k teoreme Paleya i Vinera o tselykh funktsiyakh konechnoi stepeni”, UMN, 19:1 (1964), 169–171 | MR | Zbl

[5] Katsnelson V. E., “Obobschenie teoremy Vinera–Paleya o predstavlenii tselykh funktsii konechnoi stepeni”, Teoriya funktsii, funkts. analiz i ikh prilozh., 1965, no. 1, 99–110

[6] Lyubarskii Yu. I., “Teorema Vinera–Peli dlya vypuklykh mnozhestv”, Izv. AN ArmSSR, 23:2 (1988), 163–172 | MR | Zbl

[7] Napalkov V. V., Yulmukhametov R. S., “O preobrazovaniyakh Gilberta v prostranstvakh Bergmana”, Matem. zametki, 70:1 (2001), 68–78 | MR | Zbl

[8] Merenkov S. A., “O preobrazovaniyakh Koshi v prostranstve Bergmana”, Matem. fizika, analiz i geometriya, no. 4, Kharkov, 1999, 23–31

[9] Napalkov V. V. (ml.), Yulmukhametov R. S., “O preobrazovanii Koshi funktsionalov na prostranstve Bergmana”, Matem. sb., 185:7 (1994), 77–86 | Zbl

[10] Lutsenko V. I., Yulmukhametov R. S., “Obobschenie teoremy Peli–Vinera na vesovye prostranstva”, Matem. zametki, 48:5 (1990), 80–87 | MR | Zbl

[11] Derzhavets B. A., “Prostranstva funktsii, analiticheskikh v vypuklykh oblastyakh $\mathbb C^n$ i imeyuschikh zadannoe povedenie vblizi granitsy”, DAN SSSR, 276:6 (1984), 1297–1300 | MR

[12] Napalkov V. V., “Prostranstva analiticheskikh funktsii zadannogo rosta vblizi granitsy”, Izv. AN SSSR. Ser. matem., 51:2 (1987), 287–305 | MR | Zbl

[13] Abuzyarova N. F., Yulmukhametov R. S., “Sopryazhennye prostranstva k vesovym prostranstvam analiticheskikh funktsii”, Sib. matem. zhurn., 42:1 (2001), 3–17 | MR | Zbl

[14] Epifanov O. V., “Dvoistvennost odnoi pary prostranstv analiticheskikh funktsii ogranichennogo rosta”, DAN SSSR, 319:6 (1991), 1297–1300 | Zbl

[15] Yulmukhametov R. S., “Prostranstva analiticheskikh funktsii, imeyuschikh zadannyi rost vblizi granitsy”, Matem. zametki, 32:1 (1982), 41–57 | MR | Zbl

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

[17] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 | MR | Zbl