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This article is cited in 9 scientific papers (total in 9 papers)
Real, complex and functional analysis
Method of similar operators in research of spectral properties of difference operators with growthing potential
G. V. Garkavenkoa, N. B. Uskovab a Voronezh State Pedagogical University,
Lenina st., 86,
394043, Voronezh, Russia
b Voronezh State Technical University,
Moskovsky pr., 14,
394026, Voronezh, Russia
Abstract:
We study a difference operator with a general growing potential. We obtain asymptotic formulas for the
eigenvalues, eigenvectors, and the spectral projections of such operators. We also obtain estimates for the equiconvergence of
spectral decompositions. For an invertible difference operator, we estimate off-diagonal decay of the matrix of the inverse
operator and the Fourier coefficients of the eigenvectors.
Keywords:
difference operator, similar operator method, eigenvalue, eigenvector, spectral projector.
Received July 14, 2016, published July 20, 2017
Citation:
G. V. Garkavenko, N. B. Uskova, “Method of similar operators in research of spectral properties of difference operators with growthing potential”, Sib. Èlektron. Mat. Izv., 14 (2017), 673–689
Linking options:
https://www.mathnet.ru/eng/semr815 https://www.mathnet.ru/eng/semr/v14/p673
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