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arXiv · 1201.5768

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

Iryna Egorova·Johanna Michor·Gerald Teschl
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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.

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Iryna Egorova, Johanna Michor, Gerald Teschl. 2013-06-10. Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data. https://doi.org/10.1007/s11040-012-9121-y

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