Opuscula Math. 25, no. 2 (2005), 243-260
Opuscula Mathematica
The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter
Cornelis van der Mee
Vjacheslav Pivovarchik
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.
- Cornelis van der Mee
- Università di Cagliari, Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy
- Vjacheslav Pivovarchik
- South-Ukrainian Pedagogical State University, Staroportofrankovskaya 26, 65091 Odessa, Ukraine
- Received: 2004-11-05.
