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Invariant subspaces of analytic functions. Dirichlet coefficients. (English. Russian original) Zbl 0343.46020

Funct. Anal. Appl. 7, 285-289 (1974); translation from Funkts. Anal. Prilozh. 7, No. 4, 38-43 (1973).

MSC:

46E10 Topological linear spaces of continuous, differentiable or analytic functions
46A35 Summability and bases in topological vector spaces
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References:

[1] I. F. Krasichkov-Ternovskii, ”Invariant subspaces of analytic functions, Pt. 1. Spectral synthesis on convex domains,” Matem. Sbornik,87, 459-489 (1972).
[2] I. F. Krasichkov-Ternovskii, ”Invariant subspaces of analytic functions, Pt. 2. Spectral synthesis on convex domains,” Matem. Sbornik,88, 3-30 (1972).
[3] J. P. Kahane, ”Sur quelques problèmes d’unicité et de prolongement, relatifs aux fonctions approachables par des sommes d’exponentielles,” Thèses, Durand (1954). · Zbl 0064.35903
[4] A. F. Leont’ev, ”A property of uniqueness,” Matem. Sbornik,72, 237-249 (1967).
[5] A. I. Markushevich, ”Basis in the space of analytic functions,” Matem. Sbornik,17, 211-252 (1945).
[6] J. Dieudonné and L. Schwartz, ”Duality in the (F) and (LF) spaces,” Matematika2:2, 77-101 (1958).
[7] I. F. Krasichkov-Ternovskii, ”Invariant subspaces of analytic functions, Pt. 3. Extension of spectral synthesis,” Matem. Sbornik,88, 331-352 (1972).
[8] M. G. Valiron, ”Sur les solutions des équations differentielles linéaires d’ordre infini et à coefficients constants,” Ann. Ecole Norm. Super.,46, 25-53 (1929). · JFM 55.0857.04
[9] A. F. Leont’ev, ”Series of Dirichlet polynomials and their generalizations,” Trudy Matem. In-ta im. V. A. Steklova,39, (1951).
[10] A. F. Leont’ev, ”Determination of function from the coefficients of its Dirichlet series,” Izv. Akad. Nauk SSSR, Seriya Matem,35, 125-153 (1971).
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