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On a System of Dirac Differential Equations with Discontinuity Conditions Inside an Interval

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Abstract

We study representations of solutions of the Dirac equation, properties of spectral data, and inverse problems for the Dirac operator on a finite interval with discontinuity conditions inside the interval.

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REFERENCES

  1. B. M. Levitan, and I. S. Sargsyan, Sturm-Liouville and Dirac Operators [in Russian], Nauka, Moscow (1988).

    MATH  Google Scholar 

  2. V. A. Marchenko, Sturm-Liouville Operators and Their Applications [in Russian], Naukova Dumka, Kiev (1977).

    MATH  Google Scholar 

  3. Yu. M. Berezanskii, “Uniqueness theorem in the inverse spectral problem for the Schrodinger equation,” Tr. Mosk. Mat. Obshch., 7, 3–51 (1958).

    MATH  MathSciNet  Google Scholar 

  4. L. P. Nizhnik, Inverse Scattering Problems for Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  5. M. G. Gasymov, “Inverse problem of the scattering theory for Dirac systems of order 2n,” Tr. Mosk. Mat. Obshch., 19, 41–112 (1968).

    MATH  MathSciNet  Google Scholar 

  6. M. G. Gasymov, and T. T. Dzhabiev, “Determination of a system of Dirac differential equations using two spectra,” in: Proceedings of School-Seminar on the Spectral Theory of Operators and Representations of Group Theory [in Russian], Elm, Baku (1975), pp. 46–71.

    Google Scholar 

  7. I. M. Guseinov, “On the representation of Jost solutions of a system of Dirac differential equations with discontinuous coefficients,” Izv. Akad. Nauk Azerb. SSR, No. 5, 41–45 (1999).

    Google Scholar 

  8. O. H. Hald, “Discontinuous inverse eigenvalue problems,” Comm. Pure Appl. Math., 37, 539–577 (1984).

    MATH  MathSciNet  Google Scholar 

  9. D. Shepelsky, “The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions,” Spectral Oper. Theory Rel. Topics: Adv. Sov. Math., 19, 209–232 (1994).

    MATH  MathSciNet  Google Scholar 

  10. M. Kobayashi, “A uniqueness proof for discontinuous inverse Sturm-Liouville problems with symmetric potentials,” Inverse Probl., 5, No.5, 767–781 (1989).

    Article  MATH  Google Scholar 

  11. R. Kh. Amirov, and V. A. Yurko, “On differential operators with singularity and discontinuity conditions inside an interval,” Ukr. Mat. Zh., 53, No.11, 1443–1457 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  12. V. A. Yurko, “Integral transforms connected with discontinuous boundary-value problems,” Int. Trans. Spec. Funct., 10, No.2, 141–164 (2000).

    MATH  MathSciNet  Google Scholar 

  13. B. Ya. Levin, Entire Functions [in Russian], Moscow University, Moscow (1971).

    Google Scholar 

  14. V. F. Zhdanovich, “Formulas for the zeros of Dirichlet polynomials and quasipolynomials,” Dokl. Akad. Nauk SSSR, 135, No.8, 1046–1049 (1960).

    MATH  Google Scholar 

  15. M. G. Krein, and B. Ya. Levin, “On entire almost periodic functions of exponential type,” Dokl. Akad. Nauk SSSR, 64, No.3, 285–287 (1948).

    MathSciNet  Google Scholar 

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 601–613, May, 2005.

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Amirov, R.K. On a System of Dirac Differential Equations with Discontinuity Conditions Inside an Interval. Ukr Math J 57, 712–727 (2005). https://doi.org/10.1007/s11253-005-0222-7

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  • DOI: https://doi.org/10.1007/s11253-005-0222-7

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