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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 5, Pages 75–79 (Mi ivm9002)  

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

Brief communications

On spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions

D. M. Polyakovab

a Research Institute of Mathematics, Voronezh State University, 1 Universitetskaya sq., Voronezh, 394006 Russia
b Chair of Nonlinear Oscillations, Voronezh State University, 1 Universitetskaya sq., Voronezh, 394006 Russia

Abstract: With the use of similar operator method, in this paper we study spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions. We obtain asymptotic of a spectrum and estimates of spectral decompositions. We also construct a semigroup of operators which has the opposite differential operator as a generator.

Keywords: fourth order differential operator, method of similar operators, spectrum.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:5, 64–68

UDC: 517.19
Presented by the member of Editorial Board: В. Г. Звягин
Received: 16.10.2014

Citation: D. M. Polyakov, “On spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5, 75–79; Russian Math. (Iz. VUZ), 59:5 (2015), 64–68

Citation in format AMSBIB
\Bibitem{Pol15}
\by D.~M.~Polyakov
\paper On spectral properties of fourth order differential operator with periodic and semiperiodic boundary conditions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 5
\pages 75--79
\mathnet{http://mi.mathnet.ru/ivm9002}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 5
\pages 64--68
\crossref{https://doi.org/10.3103/S1066369X15050096}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928609528}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. M. Polyakov, “Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions”, St. Petersburg Math. J., 27:5 (2016), 789–811  mathnet  crossref  mathscinet  isi  elib
    2. S. I. Mitrokhin, “Asimptotika spektra periodicheskoi kraevoi zadachi dlya differentsialnogo operatora s summiruemym potentsialom”, Tr. IMM UrO RAN, 25, no. 1, 2019, 136–149  mathnet  crossref  elib
    3. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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