Scattering Theory for Jacobi Operators with General Step-Like Quasiperiodic BackgroundI. Egorova Mathematical Division B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine J. Michor Imperial College, 180 Queen's Gate, London SW7 2BZ, UK G. Teschl Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria Received September 17, 2007 Abstract 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). |