Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra - Mykytyuk, Ya. V.; Hryniv, R. O.; Albeverio, S. (Methods of Functional Analysis and Topology, 2007)
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)× 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.