Preprint

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 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.

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

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