INVERSE SPECTRAL PROBLEMS FOR COUPLED OSCILLATING SYSTEMS: RECONSTRUCTION FROM THREE SPECTRA

We study an inverse spectral problem for a compound oscillating system consisting of a singular string and N masses joined by springs. The operator A corresponding to this system acts in L-2(0, 1) x C-N and is composed of a Sturm-Liouville operator in L-2(0, 1) with a distributional potential and a Jacobi matrix in C-N that are coupled in a special way. We solve the problem of reconstructing the system from three spectra-namely, from the spectrum of A and the spectra of its decoupled parts. A complete description of possible spectra is given.