Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

Egorova, Iryna; Michor, Johanna; Teschl, Gerald

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

Authors

Egorova, Iryna

Michor, Johanna

Teschl, Gerald

Description

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.
14 pages