Journal of Mathematical Physics, Analysis, Geometry
2008, vol. 4, No 1, pp. 33-62    ( to contents , go back )

Scattering Theory for Jacobi Operators with General Step-Like Quasiperiodic Background

I. 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
International Erwin Schrödinger Institute for Mathematical Physics Boltzmanngasse 9, 1090 Wien, Austria

G. Teschl

Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria
International Erwin Schrödinger Institute for Mathematical Physics

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).
Key words: inverse scattering, Jacobi operators, quasiperiodic, step-like.

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ISSN: 1812-9471 (Print) | ISSN: 1817-5805 (Online)