Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

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

2006-08-28

arxiv.org/abs/math/0608692v3

Inverse Problems 23, 905-918 (2007)

Mathematics

Spectral Theory

14 pages

Scientific paper

10.1088/0266-5611/23/3/004

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.

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