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Izvestiya: Mathematics, 2018, Volume 82, Issue 2, Pages 351–376
DOI: https://doi.org/10.1070/IM8623
(Mi im8623)
 

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

On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator

A. M. Savchuk

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: We study a one-dimensional Dirac system on a finite interval. The potential (a 2×2 matrix) is assumed to be complex-valued and integrable. The boundary conditions are assumed to be regular in the sense of Birkhoff. It is known that such an operator has a discrete spectrum and the system {yn}1 of its eigenfunctions and associated functions is a Riesz basis (possibly with brackets) in L2L2. Our results concern the basis property of this system in the spaces LμLμ for μ2, the Sobolev spaces W2θW2θ for θ[0,1], and the Besov spaces Bp,qθBp,qθ.
Keywords: Dirac operator, eigenfunctions and associated functions, conditional basis, Riesz basis.
Funding agency Grant number
Russian Science Foundation 17-11-01215
This work is supported by the Russian Science Foundation under grant 17-11-01215.
Received: 26.10.2016
Revised: 19.08.2017
Bibliographic databases:
Document Type: Article
UDC: 517.984.52
MSC: 34L10, 34L40, 47E05
Language: English
Original paper language: Russian
Citation: A. M. Savchuk, “On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator”, Izv. Math., 82:2 (2018), 351–376
Citation in format AMSBIB
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\by A.~M.~Savchuk
\paper On the basis property of the system of eigenfunctions and associated functions
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\jour Izv. Math.
\yr 2018
\vol 82
\issue 2
\pages 351--376
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Linking options:
  • https://www.mathnet.ru/eng/im8623
  • https://doi.org/10.1070/IM8623
  • https://www.mathnet.ru/eng/im/v82/i2/p113
  • This publication is cited in the following 10 articles:
    1. Xin Zhou, Qin Zhong, Chunyan Zhao, Learning and Analytics in Intelligent Systems, 38, Recent Trends in Educational Technology and Administration, 2024, 66  crossref
    2. A. M. Savchuk, I. V. Sadovnichaya, “Spectral Analysis of 1D Dirac System with Summable Potential and Sturm–Liouville Operator with Distribution Coefficients”, Diff Equat, 60:S2 (2024), 145  crossref
    3. D. A. Chechin, A. D. Baev, S. A. Shabrov, “Ob odnoi granichnoi zadache s razryvnymi resheniyami i silnoi nelineinostyu”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 193, VINITI RAN, M., 2021, 153–157  mathnet  crossref  elib
    4. M. Kamenskii, P. R. de Fitte, N.-Ch. Wong, M. Zvereva, “A model of deformations of a discontinuous Stieltjes string with a nonlinear boundary condition”, J. Nonlinear Var. Anal., 5:5 (2021), 737–759  crossref  mathscinet  isi
    5. A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Spectral properties of classical Dirac operators and operators with involution in homogeneous function spaces”, Differ. Equ., 57:10 (2021), 1273–1278  crossref  mathscinet  isi
    6. A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Spectral properties of the Dirac operator on the real line”, Differ. Equ., 57:2 (2021), 139–147  crossref  mathscinet  isi  scopus
    7. A. M. Savchuk, I. V. Sadovnichaya, “Spektralnyi analiz odnomernoi sistemy Diraka s summiruemym potentsialom i operatora Shturma—Liuvillya s koeffitsientami-raspredeleniyami”, Spektralnyi analiz, SMFN, 66, no. 3, Rossiiskii universitet druzhby narodov, M., 2020, 373–530  mathnet  crossref
    8. A. D. Baev, D. A. Chechin, M. B. Zvereva, S. A. Shabrov, “Stieltjes differential in impulse nonlinear problems”, Dokl. Math., 101:1 (2020), 5–8  mathnet  crossref  crossref  zmath  elib
    9. M. Kamenskii, Ch.-F. Wen, M. Zvereva, “On a variational problem for a model of a Stieltjes string with a backlash at the end”, Optimization, 69:9, SI (2020), 1935–1959  crossref  mathscinet  zmath  isi  scopus
    10. D. M. Polyakov, “Estimates of spectral gap lengths for Schrodinger and Dirac operators”, Differ. Equ., 56:5 (2020), 585–594  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:732
    Russian version PDF:104
    English version PDF:40
    References:121
    First page:43
     
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