Inverse resonance scattering for Jacobi operators

Evgeny Korotyaev

paper

Inverse resonance scattering for Jacobi operators

arXiv:0808.2805

Abstract

We consider the Jacobi operator $(J f)_{n} = a_{n - 1} f_{n - 1} + a_{n} f_{n + 1} + b_{n} f_{n}$ on $Z$ with a real compactly supported sequences $(a_{n} - 1)_{n \in Z}$ and $(b_{n})_{n \in Z}$ . We give the solution of two inverse problems (including characterization): $(a, b) \to {$ zeros of the reflection coefficient $}$ and $(a, b) \to {$ bound states and resonances $}$ . We describe the set of "iso-resonance operators $J$ ", i.e., all operators $J$ with the same resonances and bound states.