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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 673–689
DOI: https://doi.org/10.17377/semi.2017.14.058
(Mi semr815)
 

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
Full-text PDF (203 kB) Citations (9)
References:
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_а
Received July 14, 2016, published July 20, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 39A70
Language: Russian
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}
Linking options:
  • https://www.mathnet.ru/eng/semr815
  • https://www.mathnet.ru/eng/semr/v14/p673
  • This publication is cited in the following 9 articles:
    1. A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “Primenenie metoda podobnykh operatorov k nekotorym klassam raznostnykh operatorov”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 14–27  mathnet  crossref
    2. A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “O sglazhivanii operatornogo koeffitsienta differentsialnogo operatora pervogo poryadka v banakhovom prostranstve”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii  i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 3–14  mathnet  crossref
    3. A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “O matritsakh s summiruemymi diagonalyami”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 5, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 194, VINITI RAN, M., 2021, 23–37  mathnet  crossref
    4. A. G. Baskakov, G. V. Garkavenko, M. Yu. Glazkova, N. B. Uskova, “On spectral properties of one class difference operators”, Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020, 012002  crossref  isi  scopus
    5. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref  mathscinet
    6. I. A. Krishtal, N. B. Uskova, “Spektralnye svoistva differentsialnykh operatorov pervogo poryadka s involyutsiei i gruppy operatorov”, Sib. elektron. matem. izv., 16 (2019), 1091–1132  mathnet  crossref
    7. G. V. Garkavenko, “O spektralnykh svoistvakh odnogo klassa vozmuschennykh operatorov”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 57–69  mathnet  crossref
    8. 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
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
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