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, 2021, Volume 195, Pages 118–126
DOI: https://doi.org/10.36535/0233-6723-2021-195-118-126 (Mi into840) 		 
On estimates of eigenvalues of infinite block tridiagonal matrices

G. V. Garkavenkoa, N. B. Uskovab

a Voronezh State Pedagogical University
b Voronezh State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2021-195-118-126
Abstract: In this paper, we study the operators generated by infinite tridiagonal block matrices under the condition that the spectrum of the corresponding diagonal matrix is separated. Using the method of similar operators, we obtain conditions that provide the diagonalizability of the original operator (or its block diagonalizability). Also, we obtain the asymptotics of the weighted means of the eigenvalues of such operators.
Keywords: eigenvalue, method of similar operators, infinite block tridiagonal matrix.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00732-a
This work was supported by the Russian Foundation for Basic Research (project No. 19-01-00732-a).
Document Type: Article
UDC: 517.9
MSC: 47A75, 47B25, 47B36
Language: Russian
Citation: G. V. Garkavenko, N. B. Uskova, “On estimates of eigenvalues of infinite block tridiagonal matrices”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 195, VINITI, Moscow, 2021, 118–126
Citation in format AMSBIB
\Bibitem{GarUsk21}
\by G.~V.~Garkavenko, N.~B.~Uskova
\paper On estimates of eigenvalues of infinite block tridiagonal matrices
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 195
\pages 118--126
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into840}
\crossref{https://doi.org/10.36535/0233-6723-2021-195-118-126}
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