Scattering Theory for Jacobi Operators with Quasi-Periodic Background

Details Scattering Theory for Jacobi Operators with Quasi-Periodic Background Scattering Theory for Jacobi Operators with Quasi-Periodic Background

2005-06-07

arxiv.org/abs/math/0506119v1

Comm. Math. Phys. 264-3, 811-842 (2006)

Mathematics

Spectral Theory

29 pages

Scientific paper

10.1007/s00220-006-1518-7

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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