Spectral synthesis in some topological vector spaces of functions

Platonov, S.

doi:10.1090/S1061-0022-2011-01170-7

Spectral synthesis in some topological vector spaces of functions
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by S. S. Platonov
Translated by: A. Plotkin

St. Petersburg Math. J. 22 (2011), 813-833

DOI: https://doi.org/10.1090/S1061-0022-2011-01170-7

Published electronically: June 28, 2011

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Abstract:

For the topological vector function spaces of exponential growth, the spectral synthesis property is proved and the spectra of invariant subspaces are described fully.

References

Nicolas Bourbaki, Espaces vectoriels topologiques. Chapitres 1 à 5, New edition, Masson, Paris, 1981 (French). Éléments de mathématique. [Elements of mathematics]. MR 633754
Laurent Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. (2) 48 (1947), 857–929 (French). MR 23948, DOI 10.2307/1969386
Laurent Schwartz, Analyse et synthèse harmoniques dans les espaces de distributions, Canad. J. Math. 3 (1951), 503–512 (French). MR 44754, DOI 10.4153/cjm-1951-051-5
N. K. Nikol′skiĭ, Invariant subspaces in operator theory and function theory, Mathematical analysis, Vol. 12 (Russian), Akad. Nauk SSSR Vsesojuz. Inst. Naučn. i Tehn. Informacii, Moscow, 1974, pp. 199–412, 468. (loose errata) (Russian). MR 0430821
László Székelyhidi, Discrete spectral synthesis and its applications, Springer Monographs in Mathematics, Springer, Dordrecht, 2006. MR 2279454
L. R. Volevich and S. G. Gindikin, Obobshchennye funktsii i uravneniya v svertkakh, Fizmatlit “Nauka”, Moscow, 1994 (Russian, with Russian summary). MR 1379334
P. K. Raševskiĭ, Description of closed invariant subspaces in certain function spaces, Trudy Moskov. Mat. Obshch. 38 (1979), 139–185 (Russian). MR 544938
John E. Gilbert, On the ideal structure of some algebras of analytic functions, Pacific J. Math. 35 (1970), 625–634. MR 412439
G. E. Šilov, Matematicheskiĭ analiz: Vtoroĭ spetsial′nyĭkurs, Izdat. “Nauka”, Moscow, 1965 (Russian). MR 0219869
E. C. Titchmarsh, Introduction to the theory of Fourier integrals, 3rd ed., Chelsea Publishing Co., New York, 1986. MR 942661
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
B. Ya. Levin, Distribution of zeros of entire functions, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0087740
A. N. Kolmogorov and S. V. Fomin, Èlementy teorii funktsiĭ i funktsional′nogo analiza, Izdat. “Nauka”, Moscow, 1976 (Russian). Fourth edition, revised. MR 0435771
V. F. Molčanov, Elementary representations of the Laguerre group, Mat. Zametki 23 (1978), no. 1, 31–39 (Russian). MR 507244