Scattering theory for Jacobi operators with general steplike quasi-periodic background

Zh. Mat. Fiz. Anal. Geom. 4-1, 1-30 (2007).

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

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ESI Preprint 1947
arXiv:0709.2507

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