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Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data |
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| Authors: | Iryna Egorova Johanna Michor Gerald Teschl |
| Institution: | 1. Institute for Low Temperature Physics, 47, Lenin ave, 61103, Kharkiv, Ukraine 2. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Wien, Austria 3. International Erwin Schr?dinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090, Wien, Austria |
| 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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