This article is cited in 6 papers

Scattering theory for Jacobi operators with general step-like quasiperiodic background

I. Egorova^a, J. Michor^bc, G. Teschl<sup>cd

a</sup> Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
^b Imperial College, 180 Queen's Gate, London SW7 2BZ, UK
^c International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
^d Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria

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.

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

MSC: Primary 47B36, 81U40; Secondary 34L25, 39A11

Received: 17.09.2007

Language: English

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