Journal of Mathematical Sciences

, Volume 198, Issue 5, pp 625–636 | Cite as

Recovery of Discontinuities of Coefficients of the Sturm–Liouville Operator

  • A. A. Sedipkov

We study the inverse spectral problem with piecewise continuous coefficients. We prove that the asymptotics of the Jost function uniquely determines all discontinuities of the coefficients of the Sturm–Liouville operator. We present an algorithm for finding discontinuities.


Inverse Problem Periodic Function Matching Condition Acoustic Impedance Discontinuity Point 
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  1. 1.
    A. S. Alekseev and V. S. Belonosov, “The scattering of plane waves in inhomogeneous halfspace,” Appl. Math. Lett. 8. No. 2, 13–19 (1995).Google Scholar
  2. 2.
    A. S. Alekseev and V. S. Belonosov, “Direct and inverse problems associated with inclined passing of SH-waves through 1d inhomogeneous medium,” Bull. Novosib. Comput. Cent., Ser. Numer. Anal. No. 5, 1–25 (1994)Google Scholar
  3. 3.
    A. S. Alekseev and V. S. Belonosov, “Spectral methods in one-dimensional problems of the theory of wave propagation” [in Russian], Tr. Inst. Comput. Math. Math. Geophyz. SB RAS 6, 7–39 (1998).Google Scholar
  4. 4.
    A. S. Alekseev and V. S. Belonosov, “Direct and inverse problems of wave propagation through a one-dimensional inhomogeneous medium,” Eur. J. Appl. Math. 10, No. 1, 79–96 (1999).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    B. M. Levitan, Inverse Sturm–Liouville Problems [in Russian], Nauka, Moscow (1984); English transl.: VNU Science Press, Utrecht (1987).MATHGoogle Scholar
  6. 6.
    M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969); English transl.: Frederick Ungar Publ., New York (1968).Google Scholar
  7. 7.
    D. G. Shepel’sky, “The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions,” Adv. Soviet Math. 19, 209–231 (1994).MathSciNetGoogle Scholar
  8. 8.
    G. Freiling and V. Yurko, “Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point,” Inverse Probl. 18, No. 3, 757–773 (2002).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    A. I. Shestakov, “The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients” [in Russian], Sib. Mat. Zh. 44, No. 5, 1142–1162 (2003); English transl.: Sib. Math. J. 44, No. 5, 891-907 (2003).CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    B. M. Levitan, Almost Periodic Functions [in Russian], Gos. Teor. Tekhn. Lit., Moscow (1953).Google Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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