Sets of regular growth of functions in the half-plane.~I
Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 785-814.

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

We develop a theory of sets of regular growth of functions that are analytic in the upper half-plane, relative to a given indicator. A function of completely regular growth in the closed half-plane is constructed which has the given indicator and satisfies an additional condition.
@article{IM2_1995_59_4_a6,
     author = {K. G. Malyutin},
     title = {Sets of regular growth of functions in the {half-plane.~I}},
     journal = {Izvestiya. Mathematics },
     pages = {785--814},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a6/}
}
TY  - JOUR
AU  - K. G. Malyutin
TI  - Sets of regular growth of functions in the half-plane.~I
JO  - Izvestiya. Mathematics 
PY  - 1995
SP  - 785
EP  - 814
VL  - 59
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a6/
LA  - en
ID  - IM2_1995_59_4_a6
ER  - 
%0 Journal Article
%A K. G. Malyutin
%T Sets of regular growth of functions in the half-plane.~I
%J Izvestiya. Mathematics 
%D 1995
%P 785-814
%V 59
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a6/
%G en
%F IM2_1995_59_4_a6
K. G. Malyutin. Sets of regular growth of functions in the half-plane.~I. Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 785-814. http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a6/

[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):1 (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):2 (1957), 239–252 | MR | Zbl

[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 decomposition 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] Fuqlede B., Some properties of the Riesz charqe associated with a $\delta $-subharmonic function, Preprint No 23, Kobenhavus universitet, Mathematics institut, 1991, p. 1–19

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