Math. Phys. Anal. Geom. (to appear).

Scattering theory with finite-gap backgrounds: transformation operators and characteristic properties of scattering data

I. Egorova, J. Michor, and G. Teschl

Keywords: Inverse scattering, Jacobi operators, finite-gap, steplike.

Abstract: We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.

MSC: Primary 47B36, 81U40; Secondary 34L25, 39A10

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