Opuscula Mathematica

Opuscula Math.
 25
, no. 2
 (), 243-260
Opuscula Mathematica

The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter



Abstract. We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002), 315–317 [Funkts. Anal. Prilozh. 36 (2002), 74–77 (Russian)]]. Namely, for the problem of small transversal vibrations of a damped string of nonuniform stiffness with one end fixed we give the description of the spectrum and solve the inverse problem: find the conditions which should be satisfied by a sequence of complex numbers to be the spectrum of a damped string.
Keywords: damped vibrations, inhomogeneous strings, quadratic operator pencil, Hermite-Biehler functions.
Mathematics Subject Classification: 34A55.
Cite this article as:
Cornelis van der Mee, Vjacheslav Pivovarchik, The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter, Opuscula Math. 25, no. 2 (2005), 243-260
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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