Sets of regular growth of functions in a~half-plane.~II

K. G. Malyutin

Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 983-1006.

Résumé

A multiple interpolation problem is solved in the class of functions of completely regular growth in the closed upper half-plane which have a prescribed indicator and relative to a given proximal order, as well as in the class of functions analytic in the half-plane which have an indicator that does not exceed a prescribed one.

Bibliographie

[1] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[2] Govorov N. V., Kraevaya zadacha Rimana s beskonechnym indeksom, Nauka, M., 1986 | MR | Zbl

[3] Grishin A. F., “O mnozhestvakh regulyarnogo rosta tselykh funktsii”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1983, no. 40, 36–47 | MR | Zbl

[4] Grishin A. F., “O mnozhestvakh regulyarnogo rosta tselykh funktsii”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1984, no. 41, 39–55 | MR | Zbl

[5] Grishin A. F., “O mnozhestvakh regulyarnogo rosta tselykh funktsii”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1984, no. 42, 37–43 | MR | Zbl

[6] Leontev A. F., “K voprosu ob interpolirovanii v klasse tselykh funktsii konechnogo poryadka”, Matem. sb., 41 (83) (1957), 81–96 | MR | Zbl

[7] Korobeinik Yu. F., “Ob odnoi interpolyatsionnoi zadache dlya tselykh funktsii”, Izv. VUZov. Matem., 1985, no. 2, 37–45 | MR | Zbl

[8] Bratischev A. V., “Ob interpolyatsionnoi zadache v nekotorykh klassakh tselykh funktsii”, Sib. matem. zhurn., 17:1 (1976), 30–44 | MR

[9] Grishin A. F., Russakovskii A. M., “Svobodnaya interpolyatsiya tselymi funktsiyami”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1985, no. 44, 32–42 | MR | Zbl

[10] Troshin G. D., “Ob interpolirovanii funktsii, analiticheskikh v ugle”, Matem. sb., 39 (81) (1957), 239–252

[11] Levin B. Ya., Uen N. T., “Ob interpolyatsionnoi zadache v poluploskosti v klasse analiticheskikh funktsii konechnogo poryadka”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1975, no. 22, 77–85 | Zbl

[12] Uen N. T., “Interpolyatsionnaya zadacha v poluploskosti v klasse analiticheskikh funktsii konechnogo poryadka i normalnogo tipa”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1975, no. 24, 106–127 | Zbl

[13] Russakovskii A. M., “Zadacha kratnoi interpolyatsii v klasse funktsii, analiticheskikh v poluploskosti i imeyuschikh indikator ne vyshe dannogo”, DAN SSSR, 269:4 (1983), 814–817 | MR | Zbl

[14] Malyutin K. G., “Svobodnoe interpolirovanie s kratnymi uzlami v verkhnei poluploskosti”, DAN Ukrainy, 1992, no. 6, 27–29 | MR

[15] Malyutin K. G., “Zadacha kratnoi interpolyatsii v poluploskosti v klasse analiticheskikh funktsii konechnogo poryadka i normalnogo tipa”, Matem. sb., 184:2 (1993), 129–144 | MR | Zbl

[16] Jones P., “Carleson measures and the Feffermanstein decomsition of BMO(R)”, Ann. Math., 111 (1980), 197–208 | DOI | MR | Zbl

[17] Goldberg A. A., Ostrovskii I. V., “O proizvodnykh i pervoobraznykh tselykh funktsii vpolne regulyarnogo rosta”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1973, no. 18, 70–81 | MR | Zbl

[18] Fuglede B., Some properties of the Riesz charge associated with a $\delta $-subharmonic function, Preprint No 23, Obenhavus Universität, Matematics institut, 1991, p. 1–19 | MR

[19] Ronkin L. I., “Regulyarnost rosta i $D'$-asimptotika golomorfnykh funktsii v $C_+$”, Izv. VUZov. Matem., 1989, no. 6, 21–33

[20] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[21] Azarin V. S., “Ob asimptoticheskom povedenii subgarmonicheskikh funktsii”, Matem. sb., 108:2 (1979), 147–167 | MR | Zbl

[22] Grishin A. F., “O regulyarnosti rosta subgarmonicheskikh funktsii”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1968, no. 7, 59–84 | Zbl

[23] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[24] Malyutin K. G., “Mnozhestva regulyarnogo rosta v poluploskosti. Prilozheniya k interpolyatsii”, DAN Rossii, 333:3 (1993) | Zbl