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, 2022, Volume 208, Pages 15–23
DOI: https://doi.org/10.36535/0233-6723-2022-208-15-23 (Mi into990) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On spectral properties of one difference operator with involution

G. V. Garkavenkoa, N. B. Uskovab

a Voronezh State Pedagogical University
b Voronezh State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2022-208-15-23
Abstract: We consider a difference operator with involution acting in the complex Hilbert space $l_2(\mathbb{Z})$. Using the method of similar operators, we reduce it to the diagonal (block diagonal) form, which allows one to obtain various spectral characteristics of the original operator and to construct biinvariant subspaces for it.
Keywords: method of similar operators, difference operator, spectrum, spectral projector.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00732
The work of the second author was supported by the Russian Foundation for Basic Research (project No. 19-01-00732).
Document Type: Article
UDC: 517.9
MSC: 47A75, 47B25, 47B36
Language: Russian
Citation: G. V. Garkavenko, N. B. Uskova, “On spectral properties of one difference operator with involution”, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 208, VINITI, Moscow, 2022, 15–23
Citation in format AMSBIB
\Bibitem{GarUsk22}
\by G.~V.~Garkavenko, N.~B.~Uskova
\paper On spectral properties of one difference operator with involution
\inbook Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 208
\pages 15--23
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into990}
\crossref{https://doi.org/10.36535/0233-6723-2022-208-15-23}
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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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