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Scattering theory for Jacobi operators with general step-like quasiperiodic background. (English) Zbl 1177.47038

The authors develop direct and inverse scattering theory for Jacobi operators with step-like coefficients which are asymptotically close to different finite-gap quasiperiodic coefficients on different sides. They also 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:

47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
81U40 Inverse scattering problems in quantum theory
34L25 Scattering theory, inverse scattering involving ordinary differential operators
39A70 Difference operators
47A40 Scattering theory of linear operators
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