Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data
arXiv:1201.5768 · doi:10.1007/s11040-012-9121-y
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.
23 pages