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Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 673–689 (Mi semr815)  

This article is cited in 3 scientific papers (total in 3 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00197_


DOI: https://doi.org/10.17377/semi.2017.14.058

Full text: PDF file (203 kB)
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Bibliographic databases:

UDC: 517.9
MSC: 39A70
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

Citation in format AMSBIB
\Bibitem{GarUsk17}
\by G.~V.~Garkavenko, N.~B.~Uskova
\paper Method of similar operators in research of spectral properties of difference operators with growthing potential
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 673--689
\mathnet{http://mi.mathnet.ru/semr815}
\crossref{https://doi.org/10.17377/semi.2017.14.058}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Baskakov, N. B. Uskova, “Fourier method for first order differential equations with involution and groups of operators”, Ufa Math. J., 10:3 (2018), 11–34  mathnet  crossref  isi
    2. G. V. Garkavenko, A. R. Zgolich, N. B. Uskova, “Spectral analysis of a difference operator with a growing potential”, International Conference Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 973, IOP Publishing Ltd, 2018, 012053  crossref  isi  scopus
    3. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref
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