Scattering Theory for Jacobi Operators with Quasi-Periodic Background

Comm. Math. Phys. 264-3, 811-842 (2006).
[DOI: 10.1007/s00220-006-1518-7]

Scattering Theory for Jacobi Operators with Quasi-Periodic Background

I. Egorova, J. Michor, and G. Teschl

Keywords: Inverse Scattering, Toda Hierarchy.

Abstract: We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the corresponding Gel'fand-Levitan-Marchenko equation, and find minimal scattering data which determine the perturbed operator uniquely.

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

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ESI Preprint 1662
arXiv:math/0506119v1

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