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Sibirsk. Mat. Zh., 2015, Volume 56, Number 1, Pages 165–184 (Mi smj2630)  

This article is cited in 10 scientific papers (total in 10 papers)

Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients

D. M. Polyakov

Research Institute for Mathematics, Voronezh State University, Voronezh, Russia

Abstract: Using the method of similar operators, we study the spectral properties of a fourth-order differential operator with two types of classical boundary conditions. We obtain asymptotics for the spectrum and estimates for the spectral decompositions of this operator. We construct the semigroup generated by the opposite fourth-order differential operator.

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

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English version:
Siberian Mathematical Journal, 2015, 56:1, 138–154

Bibliographic databases:

UDC: 517.19
Received: 20.12.2013

Citation: D. M. Polyakov, “Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients”, Sibirsk. Mat. Zh., 56:1 (2015), 165–184; Siberian Math. J., 56:1 (2015), 138–154

Citation in format AMSBIB
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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. 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. N. B. Uskova, “On spectral properties of Sturm–Liouville operator with matrix potential”, Ufa Math. J., 7:3 (2015), 84–94  mathnet  crossref  isi  elib
    3. D. Polyakov, A. Zvyagin, “On dissipative solutions of the Jeffreys-Oldroyt-alpha equation”, Advancements in Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020089  crossref  isi  scopus
    4. G. V. Garkavenko, N. B. Uskova, “Spektralnyi analiz odnogo klassa raznostnykh operatorov s rastuschim potentsialom”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:4 (2016), 395–402  mathnet  crossref  mathscinet  elib
    5. N. B. Uskova, “On the spectral properties of a second-order differential operator with a matrix potential”, Differ. Equ., 52:5 (2016), 557–567  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. G. V. Garkavenko, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv raznostnykh operatorov s rastuschim potentsialom”, Sib. elektron. matem. izv., 14 (2017), 673–689  mathnet  crossref
    8. N. B. Uskova, G. V. Garkavenko, “Teorema o rasscheplenii lineinykh operatorov i asimptotika sobstvennykh znachenii raznostnykh operatorov s rastuschim potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 91–106  mathnet  crossref
    9. I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a fourth-order differential operator with matrix coefficients”, Differ. Equ., 54:4 (2018), 450–467  crossref  mathscinet  zmath  isi  scopus
    10. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref
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