Integral Equations and Operator Theory

, Volume 34, Issue 2, pp 234–243 | Cite as

An inverse sturm-Liouville problem by three spectra

  • Vyacheslav N. Pivovarchik


It is shown that the potential of the Sturm-Liouville equation on interval [0,a] may be restored by the spectra of three boundary problems generated by the equation on the intervals [0,a], [0, 1/2a] and [1/2a,a], respectively. The algorithm of construction is given as well as the sufficient conditions for three sequences of real numbers to be the spectra of the mentioned boundary problems. The problem on [0,a] describes small vibrations of a smooth string with fixed ends. The problems on the half-intervals describe vibrations of the same string clamped at the point of equilibrium.

MSC Primary

34A55 34B24 34B10 34L20 Secondary 73K03 


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Copyright information

© Birkhäuser Verlag 1999

Authors and Affiliations

  • Vyacheslav N. Pivovarchik
    • 1
  1. 1.Department of Higher MathematicsOdessa Academy of Civil Engineering and ArchitectureOdessaUkraine

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