This is a preview of subscription content, log in via an institution to check access.
Literature Cited
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York (1966).
Yu. A. Mitropol'skii, The Method of Averaging in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).
A. G. Baskakov, “The Krylov-Bogolyubov substitution in the theory of nonlinear perturbations of linear operators,” Preprint 80-19, Kiev (1981).
Yu. L. Daletskii (Ju. L. Daleckii) and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence (1974).
O. Friedrichs, Perturbation of Spectra in Hilbert Space, Amer. Math. Soc., Providence (1965).
N. Dunford and J. T. Schwartz, Linear Operators, Parts II and III, Wiley-Interscience (1963 and 1971).
Y. Domar, “Harmonic analysis based on certain commutative Banach algebras,” Acta Math.,96, 1–66 (1956).
Yu. I. Lyubich and V. I. Matsaev, “On operators with separable spectrum,” Math. Sb.,56, No. 4, 433–468 (1962).
Yu. I. Lyubivh, “On the spectrum of a representation of a topological Abelian group,” Dokl. Akad. Nauk SSSR,200, No. 4, 777–780 (1971).
Yu. O. Lyubich, V. I. Matsaev, and G. M. Fel'dman, “On representations with a separable spectrum,” Funkts. Anal. Prilozhen.,7, No. 2, 52–61 (1973).
I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York (1968).
Y. Domar and L.-Å. Lindahl, “Three spectral notions for representations of commutative Banach algebras,” Ann. Inst. Fourier (Grenoble),25, No. 2, 1–32 (1975).
A. G. Baskakov, “On the spectral analysis of the representations of commutative Banach algebras,” Tr. Nauchn.-Issled. Inst. Mat. Voronezh. Gos. Univ., No. 15, 1–6 (1974).
A. G. Baskakov, “On the spectral analysis in Banach modules over commutative Banach algebras,” Manuscript deposited at VINITI, No. 3058-77 Dep.
A. G. Baskakov, “Spectral mappings of Banach modules,” in: Methods of Solution of Operator Equations [in Russian], Voronezh Univ. (1978), pp. 7–12.
A. G. Baskakov, “Bernshtein-type inequalities in abstract harmonic analysis,” Sib. Mat. Zh.,20, No. 5, 942–952 (1979).
L. H. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, Princeton (1953).
N. I. Akhiezer, Theory of Approximations, Ungar, New York (1956).
D. Olesen, “On norm-continuity and compactness of spectrum,” Math. Scand.,35, 223–236 (1974).
L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
I. Ts. Gokhberg (I. C. Gohberg) and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators, Amer. Math. Soc., Providence (1969).
V. A. Sadovnichii and V. V. Dubrovskii, “Properties of the spectrum of discrete operators,” Vestn. Mosk. Gos. Univ., Mat. Mekh.,5, 37–44 (1977).
M. S. Agranovich, “Spectral properties of diffraction problems,” Supplement in: The Generalized Method of Eigenoscillations in Diffraction Theory [in Russian], N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov (eds.) Nauka, Moscow (1977), pp. 289–416.
V. I. Arnol'd, “On matrices depending on parameters,” Usp. Mat. Nauk,26, No. 2, 101–114 (1971).
V. A. Sadovnichii and V. V. Dubrovskii, “On an abstract theorem of perturbation theory, regularized trace formulas, and the zeta function of operators,” Differents. Uravn.,13, No. 7, 1264–1271 (1977).
V. A. Sadovnichii and V. V. Dubrovskii, “On certain relations for the eigenvalues of discrete operators. Trace formulas for partial differential operators,” Differents. Uravn.,13, No. 11, 2033–2042 (1977).
Additional information
Voronezh State University. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 24, No. 1, pp. 21–39, January–February, 1983.
Rights and permissions
About this article
Cite this article
Baskakov, A.G. Methods of abstract harmonic analysis in the perturbation of linear operators. Sib Math J 24, 17–32 (1983). https://doi.org/10.1007/BF00968792
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968792