Scattering Theory for Jacobi Operators with Quasi-Periodic Background
I. Egorova, J. Michor, and G. Teschl
Keywords: Inverse Scattering, Toda Hierarchy.
Abstract: We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the corresponding Gel'fand-Levitan-Marchenko equation, and find minimal scattering data which determine the perturbed operator uniquely.
MSC: Primary 47B36, 81U40; Secondary 34L25, 39A11.