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Scattering Theory for Jacobi Operators with Quasi-Periodic Background

Iryna Egorova·Johanna Michor·Gerald Teschl
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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.

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Iryna Egorova, Johanna Michor, Gerald Teschl. 2005-06-07. Scattering Theory for Jacobi Operators with Quasi-Periodic Background. https://doi.org/10.1007/s00220-006-1518-7

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