Rostyslav Kozhan: Inverse resonance problem for perturbations of Jacobi operators

We will present the full classification of spectral measures of short-range perturbations of (periodic and free) Jacobi operators. This will allow us to directly tackle the so-called inverse resonance problem: recover the Jacobi operator from the set of its eigenvalues and resonances. We solve the existence, uniqueness, and stability of this problem.