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., 2018, Volume 18, Issue 1,Pages <nobr>91

This article is cited in 2 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. Uskova^a, G. V. Garkavenko^b

^a Voronezh State Technical University, 14, Moskovsky av., Voronezh 394026, Russia
^b Voronezh State Pedagogical University, 86, Lenina St., Voronezh 394043, Russia

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.

UDC: 517.19

Received: 29.11.2016

DOI: 10.17377/PAM.2018.18.8