Inverse problems for Jacobi operators: I. Interior mass–spring perturbations in finite systems

Abstract

We consider a linear finite spring mass system which is perturbed by\nmodifying one mass and adding one spring. From knowledge of the natural\nfrequencies of the original and the perturbed systems we study when masses and\nsprings can be reconstructed. This is a problem about rank two or rank three\ntype perturbations of finite Jacobi matrices where we are able to describe\nquite explicitly the associated Green's functions. We give necessary and\nsufficient conditions for two given sets of points to be eigenvalues of the\noriginal and modified system respectively.\n