Article

**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.

** MSC2000:** Primary 47B36, 81U40; Secondary 34L25, 39A11

**Keywords:** *Inverse scattering, Jacobi operators, periodic, steplike*

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