Scattering theory for Jacobi operators with quasi-periodic background
We develop direct and inverse scattering theory for Jacobi operators which
are short range perturbations of quasi-periodic finite-gap operators.
We show existence of the transformation operator, investigate its properties,
derive the corresponding Gel'fand-Levitan-Marchenko equation, and solve the
inverse scattering problem.
Necessary and sufficient conditions for given scattering data to determine
a unique Jacobi operator are presented.
(University of Vienna)