TY  - JOUR
ID  - vanderMee2005
LB  - vanderMee2005
AU  - van der Mee, Cornelis
AU  - Pivovarchik, Vjacheslav
TI  - The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter
ST  - The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 2
SP  - 243
EP  - 260
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.2.243
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.2.243
AB  - 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.
KW  - damped vibrations
KW  - inhomogeneous strings
KW  - quadratic operator pencil
KW  - Hermite-Biehler functions
SN  - 1232-9274
ER  -