Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 171, Pages 3–18
DOI: https://doi.org/10.36535/0233-6723-2019-171-3-18 (Mi into529) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Method of similar operators in the study of spectral properties of perturbed first-order differential operators

A. G. Baskakovab, I. A. Krishtalc, N. B. Uskovad

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
b Voronezh State University
c Northern Illinois University
d Voronezh State Technical University
Full-text PDF (285 kB) Citations (3)
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DOI: https://doi.org/10.36535/0233-6723-2019-171-3-18
Abstract: In this paper, we considers first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment $[0,\omega] $ perturbed by Hilbert–Schmidt integral operators. A similarity transformation of the original operator to the operator of the block-diagonal structure is performed; this allows one to study spectral properties of the perturbed operator. The research method is the method of similar operators, which also presented in this work.
Keywords: method of similar operators, spectrum, integro-differential operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3464.2017/4.6
National Science Foundation DMS-1322127
Russian Foundation for Basic Research 19-01-00732
The work of A. G. Baskakov was supported by the Ministry of Education and Science of the Russian Federation (state assignment, project No. 1.3464.2017/4.6). The work of I. A. Krishtal was supported by the National Science Foundation of the USA (project DMS-1322127). The work of N. B. Uskova was supported by the Russian Foundation for Basic Research (project No. 19-01-00732).
Document Type: Article
UDC: 517.9
MSC: 35L75, 35Q53, 37K10, 37K35
Language: Russian
Citation: A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Method of similar operators in the study of spectral properties of perturbed first-order differential operators”, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 171, VINITI, Moscow, 2019, 3–18
Citation in format AMSBIB
\Bibitem{BasKriUsk19}
\by A.~G.~Baskakov, I.~A.~Krishtal, N.~B.~Uskova
\paper Method of similar operators in the study of spectral properties of perturbed first-order differential operators
\inbook Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 171
\pages 3--18
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into529}
\crossref{https://doi.org/10.36535/0233-6723-2019-171-3-18}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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