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Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data

Iryna Egorova, Johanna Michor, and Gerald Teschl

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 allows unique solvability of the inverse scattering problem for perturbations with finite second moment.

MSC2010: Primary 47B36, 81U40; Secondary 34L25, 39A10
Keywords: Inverse scattering, Jacobi operators, finite-gap, steplike

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