Scattering theory for Jacobi operators with quasi-periodic background

Johanna Michor
(University of Vienna)

Abstract: 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.