Geodesic
The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 91-106

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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. 
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     title = {The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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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. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 91-106. http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a7/