Iryna Egorova, Johanna Michor, and Gerald Teschl
Scattering Theory for Jacobi Operators with General Steplike Quasi-Periodic Background
(72K, LaTeX2e)

ABSTRACT.  We develop direct and inverse scattering theory for Jacobi operators 
with steplike coefficients which are asymptotically close to 
different finite-gap quasi-periodic coefficients on different sides. 
We give a complete characterization of the scattering data, which 
allow unique solvability of the inverse scattering problem in the 
class of perturbations with finite first moment.