Inverse Problems 23, 905-918 (2007) [DOI: 10.1088/0266-5611/23/3/004]
Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background
Iryna Egorova, Johanna Michor, and Gerald Teschl
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.