**Inverse Problems**

**23**, 905-918 (2007)

[DOI: 10.1088/0266-5611/23/3/004]

## Scattering theory for Jacobi operators with steplike quasi-periodic background

### I. Egorova, J. Michor, and G. Teschl

**Keywords:** Inverse scattering, Jacobi operators.

**Abstract:**
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..

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

**ESI Preprint** 1835

**arXiv:math/0608692v3**

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