Inverse problems for Jacobi operators II: Mass perturbations of   semi-infinite mass-spring systems
  We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations. Necessary and sufficient conditions for two real sequences to be the spectra of two modified systems are provided. 
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva
math-ph math.MP