Scattering theory for Jacobi operators with general steplike quasi-periodic background
I. Egorova, J. Michor, and G. Teschl
Keywords: Inverse scattering, Jacobi operators, quasi-periodic, periodic, steplike.
Abstract: We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite first moment.
MSC: Primary 47B36, 81U40; Secondary 34L25, 39A11