Article

**Oper. Matrices 3, 205-214 (2009)**[DOI: 10.7153/oam-03-11]

## Reconstruction of the Transmission Coefficient for Steplike Finite-Gap Backgrounds

### Iryna Egorova and Gerald Teschl

We consider scattering theory for one-dimensional Jacobi operators with respect to steplike
quasi-periodic finite-gap backgrounds and show how the transmission coefficient can be reconstructed from
minimal scattering data. This generalizes the Poisson-Jensen formula for the classical constant background
case.

** MSC91:** Primary 30E20, 30F30; Secondary 34L25, 47B36

**Keywords:** *Jacobi operators, scattering theory, periodic, Abelian integrals*

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