Geodesic
Spectral synthesis on systems of convex domains. Extension of the synthesis
Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 87-105 
I. F. Krasichkov-Ternovskii. Spectral synthesis on systems of convex domains. Extension of the synthesis. Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 87-105. http://geodesic.mathdoc.fr/item/SM_1981_40_1_a4/
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     author = {I. F. Krasichkov-Ternovskii},
     title = {Spectral synthesis on systems of convex domains. {Extension} of the synthesis},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of homogeneous convolution equations is considered in convex Domains $G_1,\dots, G_q\subset G$. Earlier (Mat. Sb. (N. S.) 111(153) (1980), 3–41) the author studied the following problem of spectral synthesis: under what conditions can every solution $f=(f_1,\dots,f_q)$ of such a system be approximated by linear combinations of elementary solutions inside $G_1,\dots,G_q$? In the present paper the following problem of the extension of the synthesis is considered: under what conditions does a solution $f=(f_1,\dots,f_q)$ admit approximation not only in $G_1,\dots,G_q$ but also in larger domains $G'_1\supset G_1$, $\dots$, $G'_q\supset G_q$ which are contained in the domains of existence of the components $f_1,\dots,f_q$? Bibliography: 8 titles.

[1] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii. I. Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87(129) (1972), 459–487

[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), 44–66 | 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] I. F. Krasichkov-Ternovskii, “Spektralnyi sintez analiticheskikh funktsii na sistemakh vypuklykh oblastei”, Matem. sb., 111(153) (1980), 3–41 | MR

[7] I. F. Krasichkov-Ternovskii, “Invariantnye podprostranstva analiticheskikh funktsii. Koeffitsienty Dirikhle”, Funkts. analiz, 7:4 (1973), 38–43 | MR

[8] A. F. Leontev, “Ob odnom svoistve edinstvennosti”, Matem. sb., 72(144) (1967), 237–249 | MR