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

Mathematics – Spectral Theory

Scientific paper

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23 pages

Scientific paper

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.

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