Spectral synthesis on systems of convex domains. Extension of the synthesis
Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 87-105
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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.
@article{SM_1981_40_1_a4,
author = {I. F. Krasichkov-Ternovskii},
title = {Spectral synthesis on systems of convex domains. {Extension} of the synthesis},
journal = {Sbornik. Mathematics},
pages = {87--105},
publisher = {mathdoc},
volume = {40},
number = {1},
year = {1981},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1981_40_1_a4/}
}
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/