Interpolation by means of special classes of entire functions and related expansions in series of exponentials
Izvestiya. Mathematics , Tome 9 (1975) no. 3, pp. 621-662.

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

In this paper, we study the problems of interpolation by means of entire functions of exponential type which satisfy special restrictions on their growth, and the relationship of these problems to Dirichlet series expansions in an arbitrary convex polygon of functions from a Smirnov space. Bibliography: 26 items.
@article{IM2_1975_9_3_a8,
     author = {B. Ya. Levin and Yu. I. Lyubarskii},
     title = {Interpolation by means of special classes of entire functions and related expansions in series of exponentials},
     journal = {Izvestiya. Mathematics },
     pages = {621--662},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a8/}
}
TY  - JOUR
AU  - B. Ya. Levin
AU  - Yu. I. Lyubarskii
TI  - Interpolation by means of special classes of entire functions and related expansions in series of exponentials
JO  - Izvestiya. Mathematics 
PY  - 1975
SP  - 621
EP  - 662
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a8/
LA  - en
ID  - IM2_1975_9_3_a8
ER  - 
%0 Journal Article
%A B. Ya. Levin
%A Yu. I. Lyubarskii
%T Interpolation by means of special classes of entire functions and related expansions in series of exponentials
%J Izvestiya. Mathematics 
%D 1975
%P 621-662
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a8/
%G en
%F IM2_1975_9_3_a8
B. Ya. Levin; Yu. I. Lyubarskii. Interpolation by means of special classes of entire functions and related expansions in series of exponentials. Izvestiya. Mathematics , Tome 9 (1975) no. 3, pp. 621-662. http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a8/

[1] Levin B. Ya., Lyubarskii Yu. I., “Interpolyatsiya tselymi funktsiyami eksponentsialnogo tipa i ee prilozheniya k razlozheniyam v ryady po eksponentam”, Funktsionalnyi analiz i ego prilozheniya, 8:2 (1974), 85–86 | Zbl

[2] 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

[3] Levin B. Ya., Tselye funktsii, MGU, M., 1971

[4] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L^2(-\pi,\pi)$”, Zapiski fiz.-mat. fak-ta Kharkovskogo gos. un-ta i Kharkovsk. matem. ob-va, ser. 4, 27, 1961, 39–48

[5] Levin B. Ya., “Interpolyatsiya tselymi funktsiyami eksponentsialnogo tipa”, Matematicheskaya fizika i funktsionalnyi analiz, no. 1, FTINT AN USSR, Kharkov, 1969, 136–146 | MR

[6] Sedletskii A. M., “O biortogonalnykh razlozheniyakh po pokazatelnym funktsiyam”, Izv. AN SSSR. Ser. matemat., 36 (1972), 583–590 | MR

[7] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GTTL, M., 1956

[8] Guter R. S., Ulyanov L. L., “O novykh rezultatakh v teorii ortogonalnykh ryadov”, v kn. S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[9] Golovin V. D., “O biortogonalnykh razlozheniyakh v $L^2$ po lineinym kombinatsiyam pokazatelnykh funktsii”, Zapiski mekh.-mat. fak-ta Kharkovskogo gos. un-ta i Kharkovsk. Matem. o-va, ser. 4, 30, 1964, 18–29 | MR

[10] Katsnelson V. E., “O bazisakh iz pokazatelnykh funktsii v $L^2$”, Funktsionalnyi analiz i ego prilozheniya, 5:1 (1971), 37–47 | MR

[11] Pavlov B. S., “Spektralnyi analiz differentsialnogo operatora s “razmazannym” granichnym usloviem”, Problemy matematicheskoi fiziki, no. 6, LGU, 1973, 101–119

[12] Delsart J., “Les fonctions “moyenne-périodiques””, J. Math. Pures. Appl., 14 (1935), 403–453 | Zbl

[13] Schwartz L., “Theorie general des fonctions moyenne-périodiques”, Ann. Math., 48:4 (1957), 857–928 | DOI | MR

[14] Levinson N., Gap and density theorems, Amer. Math. Soc. Coll. Publ., New York, 1940 | MR

[15] Sedletskii A. M., “Negarmonicheskie ryady Fure”, Sib. matem. zh., XII:5 (1971), 1100–1114

[16] Plancherel A., Polya G., “Fonctions entieres et intégrates Fourier multiples”, Comm. Math. Helv., 10 (1936), 110–163 | DOI | MR

[17] Leontev A. F., “O predstavlenii analiticheskikh, funktsii v zamknutoi vypukloi oblasti ryadami Dirikhle”, Izv. AN SSSR. Ser. matem., 37 (1973), 577–592 | MR

[18] Leontev A. F., “O predstavlenii analiticheskikh funktsii v mnogougolnoi zamknutoi oblasti ryadami Dirikhle”, Izv. AN SSSR. Ser. matem., 38 (1974), 127–138 | MR

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

[20] Titchmarsh E., Vvedenie v teoriyu integralov Fure, GTTL, M., L., 1948

[21] Cartwright M., “On certain integral functions of order 1”, Quartely J. Math. (Oxford Ser.), 7 (1936), 46–55 | DOI | Zbl

[22] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GTTL, M., L., 1950

[23] Leontev A. F., “Ob usloviyakh razlozheniya analiticheskikh funktsii v ryady Dirikhle”, Izv. AN SSSR. Ser. matem., 36 (1972), 1282–1295 | MR

[24] Leontev A. F., “O predstavlenii proizvolnykh funktsii ryadami Dirikhle”, Dokl. AN SSSR, 164:1 (1965), 40–43 | MR

[25] Leontev A. F., “Predstavlenie funktsii obobschennymi ryadami Dirikhle”, Uspekhi matem. nauk, XXIV:2 (1969), 97–165 | MR

[26] Leontev A. F., “O predstavlenii analiticheskikh funktsii v otkrytoi oblasti ryadami Dirikhle”, Matem. sb., 81:4 (1970), 552–579 | MR