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An inverse eigenvalue problem for one dimensional Dirac operators

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Abstract

We consider an inverse eigenvalue problem for Dirac operators on finite intervals. We show that if for a \({\mu\in\mathbb{C}}\) the system \({\{\exp{2i\lambda_nx}}\), \({\exp{2i\mu x}\}}\) is closed in \({L^p[-\pi,\pi]}\), then there is at most one \({L^p}\)-potential with the eigenvalues \({\lambda_n}\). The result corresponds to the case of Schrödinger operators.

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References

  1. Albeverio S., Hryniv R., Mykytyuk Ya.: Inverse spectral problems for Dirac operators with summable potentials. Russian J. Math. Phys. 12, 406–423 (2005)

    MathSciNet  MATH  Google Scholar 

  2. Arutyunyan T. N.: Transformation operators for the canonical Dirac system. Differ. Equ. 44, 1041–1052 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Horváth M.: On a theorem of Ambarzumian. Proc. Royal Soc. Edinburgh 131A, 899–907 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Horváth M.: On the inverse spectral theory of Schrödinger and Dirac operators. Trans. Amer. Math. Soc. 353, 4155–4171 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Horváth M.: Inverse spectral problems and closed exponential systems. Ann. Math. 162, 885–918 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kiss M.: An n-dimensional Ambarzumian type theorem for Dirac operators. Inverse Problems 20, 1593–1597 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. N. Levinson, Gap and Density Theorems, AMS Coll. Publ. vol. XXVI, AMS (New York, 1940).

  8. B. M. Levitan and I. S. Sargsjan, Sturm–Liouville and Dirac operators, Kluwer Academic (Dordrecht–Boston, 1991).

  9. V. A. Marchenko, Sturm-Liouville Operators and Applications, translated from the Russian by A. Iacob, Operator Theory: Advances and Applications, 22, Birkhäuser Verlag (Basel, 1986).

  10. B. Thaller, The Dirac Equation, Springer-Verlag (Berlin–Heidelberg–New York, 1992).

  11. Zhaoying Wei, Yongxia Guo and Guangsheng Wei, Incomplete inverse spectral and nodal problems for Dirac operator, Adv. Difference Equations, 2015 (2015), 188.

  12. R. M. Young, An Introduction to Nonharmonic Fourier Series, Academic Press (New York, 1980).

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  1. Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics, 1111, Budapest, Műegyetem rkp. 3-9, Hungary

    M. Kiss

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  1. M. Kiss
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Kiss, M. An inverse eigenvalue problem for one dimensional Dirac operators. Acta Math. Hungar. 152, 326–335 (2017). https://doi.org/10.1007/s10474-017-0733-3

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  • DOI: https://doi.org/10.1007/s10474-017-0733-3

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