Siberian Journal of Pure and Applied Mathematics
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Siberian Journal of Pure and Applied Mathematics, 2018, Volume 18, Issue 1, Pages 91–106
DOI: https://doi.org/10.17377/PAM.2018.18.8 (Mi vngu466) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential

N. B. Uskovaa, G. V. Garkavenkob

a Voronezh State Technical University, 14, Moskovsky av., Voronezh 394026, Russia
b Voronezh State Pedagogical University, 86, Lenina St., Voronezh 394043, Russia
Full-text PDF (166 kB) Citations (5)
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DOI: https://doi.org/10.17377/PAM.2018.18.8
Abstract: We consider a difference operator with a growing potential in the Hilbert space of square summable complex bilateral sequences and study the asymptotic behavior of eigenvalues under three different conditions on the potential. The main results are btained by using the decomposition method of similar operators.
Keywords: difference operator, eigenvalues, eigenvectors, spectral projection, method of similar operators, the operator splitting.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00197_а
The work is supported by the Russian Foundation for Basic Research (project No. 16-01-00197)
Received: 29.11.2016
English version:
Journal of Mathematical Sciences, 2020, Volume 246, Issue 6, Pages 812–827
DOI: https://doi.org/10.1007/s10958-020-04784-3
Document Type: Article
UDC: 517.19
Language: Russian
Citation: N. B. Uskova, G. V. Garkavenko, “The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential”, Sib. J. Pure and Appl. Math., 18:1 (2018), 91–106; J. Math. Sci., 246:6 (2020), 812–827
Citation in format AMSBIB
\Bibitem{UskGar18}
\by N.~B.~Uskova, G.~V.~Garkavenko
\paper The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 1
\pages 91--106
\mathnet{http://mi.mathnet.ru/vngu466}
\crossref{https://doi.org/10.17377/PAM.2018.18.8}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 246
\issue 6
\pages 812--827
\crossref{https://doi.org/10.1007/s10958-020-04784-3}
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  • https://www.mathnet.ru/eng/vngu/v18/i1/p91
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал чистой и прикладной математики
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