Scattering Theory for Jacobi Operators with General Step-Like Quasiperiodic Background
Mathematical Division B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine
Imperial College, 180 Queen's Gate, London SW7 2BZ, UK
Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria
Received September 17, 2007
We develop direct and inverse scattering theory for Jacobi operators with step-like coeffscients which are asymptotically close to different finite-gap quasiperiodic 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.
Mathematics Subject Classification 2000: 47B36, 81U40 (primary); 34L25, 39A11 (secondary).