Geodesic
Spectral synthesis of analytic functions on systems of convex domains
Sbornik. Mathematics, Tome 39 (1981) no. 1, pp. 1-35 
I. F. Krasichkov-Ternovskii. Spectral synthesis of analytic functions on systems of convex domains. Sbornik. Mathematics, Tome 39 (1981) no. 1, pp. 1-35. http://geodesic.mathdoc.fr/item/SM_1981_39_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In a complex domain the problem of approximating solutions of systems of homogeneous convolution equations by linear combinations of elementary solutions is considered. This problem can be solved in the framework of the general problem of spectral synthesis with the use of the technique of submodules, developed in earlier papers of the author. Bibliography: 14 titles.

[1] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii I. Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87(129) (1972), 459–489

[2] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii II. Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 88(130) (1972), 3–30

[3] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii III. O rasprostranenii spektralnogo sinteza”, Matem. sb., 88(130) (1972), 331–352

[4] I. F. Krasichkov-Ternovskii, “Lokalnoe opisanie zamknutykh idealov i podmodulei analiticheskikh funktsii odnoi peremennoi I”, Izv. AN SSSR, seriya matem., 43 (1979), 87–110 | MR

[5] I. F. Krasichkov-Ternovskii, “Lokalnoe opisanie zamknutykh idealov i podmodulei analiticheskikh funktsii odnoi peremennoi II”, Izv. AN SSSR, seriya matem., 43 (1979), 309–341 | MR

[6] B. Malgrange, “Existence et approximation des solutions des équations aux derivées partielles et des equations de convolution”, Ann. Inst. Fourier, 6 (1955), 271–354 | MR

[7] L. Ehrenpreis, “Mean periodic functions”, Amer. J. Math., 77:2 (1955), 293–326 | DOI | MR

[8] D. I. Gurevich, “Kontrprimery k probleme L. Sh. Shvartsa”, Funkts. analiz, 9:2 (1975), 29–35 | MR | Zbl

[9] V. V. Napalkov, “Ob odnoi teoreme edinstvennosti v teorii funktsii mnogikh kompleksnykh peremennykh i odnorodnykh uravneniyakh tipa svertki v trubchatykh oblastyakh”, Izv. AN SSR, seriya matem., 40:1 (1976), 115–132 | MR | Zbl

[10] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956

[11] L. Hörmander, “Generators for some rings of analytic functions”, Bull. Amer. Math. Soc., 73:6 (1967), 943–949 | DOI | MR | Zbl

[12] I. F. Krasichkov, “Sravnenie tselykh funktsii konechnogo poryadka po raspredeleniyu ikh kornei”, Matem. sb., 70(102) (1966), 198–230 | Zbl

[13] V. A. Tkachenko, “Ob operatorakh, kommutiruyuschikh s obobschennym differentsirovaniem v prostranstvakh analiticheskikh funktsionalov s zadannym indikatorom rosta”, Matem. sb., 102(144) (1977), 435–456 | Zbl

[14] I. F. Krasichkov-Ternovskii, “Lokalnoe opisanie zamknutykh podmodulei i problema sverkhnasyschennosti”, Zapiski nauchnykh seminarov LOMI, 81 (1978), 133–136