Abstract:
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.
A. P. Khromov, “Finite-dimensional perturbations of Volterra operators”, Journal of Mathematical Sciences, 138:5 (2006), 5893–6066
I. F. Krasichkov-Ternovskii, “Approximation theorem for a homogeneous
vector convolution equation”, Sb. Math., 195:9 (2004), 1271–1289
I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Russian Math. Surveys, 58:1 (2003), 31–108
A. B. Shishkin, “Spectral synthesis for systems of differential operators with
constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898
I. F. Krasichkov-Ternovskii, A. B. Shishkin, “Local description of closed submodules of a special module of entire functions of exponential type”, Sb. Math., 192:11 (2001), 1621–1638
I. F. Krasichkov-Ternovskii, “Spectral synthesis and local description for several variables”, Izv. Math., 63:4 (1999), 729–755
I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. II”, Sb. Math., 188:6 (1997), 853–892
I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. I”, Sb. Math., 188:2 (1997), 195–226
I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. III”, Sb. Math., 188:10 (1997), 1439–1479
S. G. Merzlyakov, “Spectral synthesis for the differentiation operator on systems of curvilinear strips”, Sb. Math., 186:5 (1995), 711–728
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. II. The module method”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 1–15
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. III: Ample submodules”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 165–188
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. IV: Synthesis”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 407–426
A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. I: A duality theorem”, Math. USSR-Sb., 74:2 (1993), 309–335
I. F. Krasichkov-Ternovskii, “Abstract methods for a local description of closed submodules of analytic functions”, Math. USSR-Sb., 71:2 (1992), 481–497
I. F. Krasichkov-Ternovskii, “Spectral synthesis on systems of convex domains. Extension of the synthesis”, Math. USSR-Sb., 40:1 (1981), 87–105
I. F. Krasichkov-Ternovskii, “Spectral synthesis on systems of unbounded convex domains”, Math. USSR-Sb., 39:3 (1981), 343–357
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