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Mat. Zametki, 2011, Volume 89, Issue 6, Pages 885–893 (Mi mz8657)  

This article is cited in 6 scientific papers (total in 6 papers)

Solution of the Inverse Quasiperiodic Problem for the Dirac System

I. M. Nabievab

a Baku State University
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: We present a complete solution of the inverse problem of spectral analysis for the Dirac operator with quasiperiodic boundary conditions. We prove a uniqueness theorem for the solution of the inverse problem and obtain necessary and sufficient conditions for a sequence of real numbers to be the spectrum of a quasiperiodic Dirac problem.

Keywords: inverse spectral problem, Dirac operator, quasiperiodic Dirac problem, Lyapunov function, boundary-value problem, spectral data, Bernstein's inequality

DOI: https://doi.org/10.4213/mzm8657

Full text: PDF file (465 kB)
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English version:
Mathematical Notes, 2011, 89:6, 845–852

Bibliographic databases:

Document Type: Article
UDC: 517.984
Received: 02.12.2009
Revised: 13.05.2010

Citation: I. M. Nabiev, “Solution of the Inverse Quasiperiodic Problem for the Dirac System”, Mat. Zametki, 89:6 (2011), 885–893; Math. Notes, 89:6 (2011), 845–852

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. I. M. Nabiev, “Determination of the diffusion operator on an interval”, Colloq. Math., 134:2 (2014), 165–178  crossref  mathscinet  zmath  isi  scopus
    2. T. Sh. Abdullaev, I. M. Nabiev, “An algorithm for reconstructing the Dirac operator with a spectral parameter in the boundary condition”, Comput. Math. Math. Phys., 56:2 (2016), 256–262  mathnet  crossref  crossref  isi  elib
    3. Akcay O., Mamedov Kh.R., “Inverse Spectral Problem For Dirac Operators By Spectral Data”, Filomat, 31:4 (2017), 1065–1077  crossref  mathscinet  isi  scopus
    4. Mamedov Kh.R., Akcay O., “Inverse Problem For a Class of Dirac Operators By the Weyl Function”, Dyn. Syst. Appl., 26:1 (2017), 183–195  mathscinet  isi
    5. Currie S., Roth T.T., Watson B.A., “Eigenvalue Interlacing For First Order Differential Systems With Periodic 2 X 2 Matrix Potentials and Quasi-Periodic Boundary Conditions”, Oper. Matrices, 12:2 (2018), 489–499  crossref  mathscinet  zmath  isi
    6. Currie S., Roth T.T., Watson B.A., “Inverse Problems For First-Order Differential Systems With Periodic 2 X 2 Matrix Potentials and Quasi-Periodic Boundary Conditions”, Math. Meth. Appl. Sci., 41:15, SI (2018), 5985–5988  crossref  mathscinet  zmath  isi  scopus
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