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
E-mail: egorova@ilt.kharkov.ua

J. Michor

Imperial College, 180 Queen's Gate, London SW7 2BZ, UK
International Erwin Schrödinger Institute for Mathematical Physics Boltzmanngasse 9, 1090 Wien, Austria
E-mail: Johanna.Michor@esi.ac.at

G. Teschl

Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria
International Erwin Schrödinger Institute for Mathematical Physics
E-mail: Gerald.Teschl@univie.ac.at

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

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