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Algebra i Analiz, 2019, Volume 31, Issue 4, Pages 16–47 (Mi aa1661)  
This article is cited in 8 scientific papers (total in 8 papers)

Research Papers

On the asymptotics of eigenvalues of a third-order differential operator

I. N. Braeutigama, D. M. Polyakovbc

a Northern (Arctic) Federal University named after M. V. Lomonosov, Arkhangelsk
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
Full-text PDF (326 kB) Citations (8)
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Abstract: We consider a third-order nonselfadjoint differential operator with square summable coefficients whose domain is defined by quasiperiodic boundary conditions. For this operator, using the method of similar operators, we obtain an asymptotic behavior of eigenvalues, estimates of the deviations of spectral projections, and the equiconvergence of spectral decompositions.
Keywords: third-order differential operator, spectrum, asymptotic behavior of eigenvalues, equiconvergence of spectral decompositions.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.12791.2018/12.2
МК-1056.2018.1
Russian Foundation for Basic Research 18-31-00205
The work of the first author was supported by the Ministry of Education and Science of Russia and DAAD in the framework of the program “Mikhail Lomonosov” (no. 1.12791.2018/12.2).
Received: 17.05.2018
English version:
St. Petersburg Mathematical Journal, 2020, Volume 31, Issue 4, Pages 585–606
DOI: https://doi.org/10.1090/spmj/1616
Bibliographic databases:
Document Type: Article
MSC: Primary 47A75; Secondary 47A10, 65L10
Language: Russian
Citation: I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a third-order differential operator”, Algebra i Analiz, 31:4 (2019), 16–47; St. Petersburg Math. J., 31:4 (2020), 585–606
Citation in format AMSBIB
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\pages 16--47
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\vol 31
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\pages 585--606
\crossref{https://doi.org/10.1090/spmj/1616}
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Linking options:
  • https://www.mathnet.ru/eng/aa1661
  • https://www.mathnet.ru/eng/aa/v31/i4/p16
    • This publication is cited in the following 8 articles:
    1. Natalia P. Bondarenko, “Inverse Spectral Problem for the Third-Order Differential Equation”, Results Math, 78:5 (2023)  crossref
    2. Maozhu Zhang, Kun Li, Yicao Wang, “Regular approximation of singular third-order differential operators”, Journal of Mathematical Analysis and Applications, 521:1 (2023), 126940  crossref
    3. Natalia Pavlovna Bondarenko, “Linear differential operators with distribution coefficients of various singularity orders”, Math Methods in App Sciences, 46:6 (2023), 6639  crossref
    4. 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
    5. Natalia P. Bondarenko, “Reconstruction of Higher-Order Differential Operators by Their Spectral Data”, Mathematics, 10:20 (2022), 3882  crossref
    6. D. M. Polyakov, “Spectral Asymptotics of Two-Term Even Order Operators with Involution”, J Math Sci, 260:6 (2022), 806  crossref
    7. N. P. Bondarenko, “Inverse spectral problems for arbitrary-order differential operators with distribution coefficients”, Mathematics, 9:22 (2021), 2989  crossref  mathscinet  isi  scopus
    8. D. M. Polyakov, “Formula for Regularized Trace of a Second Order Differential Operator with Involution”, J Math Sci, 251:5 (2020), 748  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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