1211.4274 (Rostyslav Kozhan)

Inverse Spectral theorem and point perturbations of eventually periodic
Jacobi matrices    [PDF]

Rostyslav Kozhan

We discuss properties of resonances for exponentially small perturbations of periodic and free Jacobi matrices. We show that eventually periodic Jacobi matrices are uniquely determined by the locations of eigenvalues and resonances, and we fully characterize all possible con?figurations of eigenvalues and resonances. We show that it is always possible to add/remove a point mass to/from the spectrum of a Jacobi matrix without decreasing the exponential rate of proximity from the isospectral torus.

View original: http://arxiv.org/abs/1211.4274