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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vngu466
https://www.mathnet.ru/eng/vngu/v18/i1/p91
This publication is cited in the following 5 articles:
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