On the expansion of analytic functions in a series of elementary solutions of a convolution equation
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 597-605 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions for the representation of arbitrary analytic functions in the form of an exponential series are studied.
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V. V. Napalkov; A. W. Komarov. On the expansion of analytic functions in a series of elementary solutions of a convolution equation. Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 597-605. http://geodesic.mathdoc.fr/item/SM_1991_69_2_a16/

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

[2] Krasichkov-Ternovskii I. F., “Odna geometricheskaya lemma, poleznaya v teoriya tselykh funktsii, i teoremy tipa Levinsona”, Matem. zametki, 24:4 (1978), 531–546 | MR

[3] Napalkov V. V., “O bazise v prostranstve reshenii uravneniya svertki”, Matem. zametki, 43:1 (1988), 44–55 | MR | Zbl

[4] Napalkov V. V., “Diskretnye slabo dostatochnye mnozhestva v nekotorykh prostranstvakh tselykh funktsii”, Izv. AN SSSR. Ser. matem., 45:5 (1981), 1088–1099 | MR | Zbl

[5] Sebashtyan-i-Silva Zh., “O nekotorykh klassakh lokalno-vypuklykh prostranstv, vazhnykh v prilozheniyakh”, Matematika, 1:1 (1957), 60–78

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

[7] Meise R., “Sequence space representation for $(DFN)$ -algebras of entire functions modulo closed ideals”, J. Reine Angew. Math., 282 (1985), 59–95 | MR

[8] Grothendieck A., “Sur les espaces $(F)$ et $(DF)$”, Summa Bras. Math., 1954, 57–123 | MR

[9] Leontev A. F., “O predstavlenii analiticheskikh funktsii v otkrytoi oblasti ryadami Dirikhle”, Matem. sb., 81(123) (1970), 552–579 | MR

[10] Leontev A. F., “Ob usloviyakh razlozhimosti analiticheskoi funktsii v ryad Dirikhle”, Izv. AN SSSR. Ser. matem., 36 (1972), 1282–1295 | MR

[11] Napalkov V. V., Uravneniya svertki v mnogomernykh prostranstvakh, Nauka, M., 1982 | MR

[12] Napalkov V. V., “O diskretnykh dostatochnykh mnozhestvakh v nekotorykh prostranstvakh tselykh funktsii”, DAN SSSR, 250:4 (1980), 809–812 | MR | Zbl

[13] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 325–356 | MR

[14] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, UMN, 36:1 (1981), 73–126 | MR | Zbl