Abstract
In the paper a wide class of nonself-adjoint operators is considered, the characteristic function of which are bounded in the upper half-plane. A functional model is constructed, an absolutely continuous subspace,spectrum, and projectors are defined (which are calculated in terms of the characteristic function and the initial operator). The method of embedding, which is given, of the initial operator into a model theory, and the calculation of projectors are convenient in the study of a wide class of differential operators.
Similar content being viewed by others
References
B. S. Pavlov, Self-adjoint dilations of a dissipative Schrödinger operator and its expansion with respect to the eigenfunctions, Mat. Sb.102, No. 4, 511–536 (1977).
B. S. Pavlov, “Dilation theory and spectral analysis of nonself-adjoint differential operators,” Abstracts of the 7th Winter School on Mathematical Programming and Related Problems. TsÉMI AN SSSR, Moscow (1976), Part 2: Theory of operators in linear spaces, pp. 3–69.
S. N. Naboko, “Absolutely continuous spectrum of a nondissipative operator and a functional model 2,” Notes of Scientific Seminars LOMI,73, 118–135 (1977).
A. V. Kuzhel', “Proper extensions of Hermitian operators in a space with a nondefinite metric,” Dokl. Akad. Nauk SSSR, Ser. Mat.,265, No. 5, 1059–1061 (1982).
V. A. Derkach and M. M. Malamud, The Weyl Function of a Hermitian Operator and Its Connection with the Characteristic Function, DonFTI, Donetsk (1985).
B. W. McEnnis, “Models for operators with bounded characteristic function,” Acta Sci. Math.,43, No. 1–2, 71–87 (1981).
Author information
Authors and Affiliations
Additional information
Translated from Dinamicheskie Sistemy, No. 7, pp. 109–114, 1988.
Rights and permissions
About this article
Cite this article
Petrov, A.M. Spectral projectors of some classes of nonself-adjoint operators. J Math Sci 65, 1575–1578 (1993). https://doi.org/10.1007/BF01097667
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097667