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

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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. Garkavenko^a, N. B. Uskova^b

^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)

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

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:

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
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
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
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
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
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
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
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
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

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

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