Opuscula Math. 25, no. 2 (2005), 243-260
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.