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

TeX file (29k) or pdf file (321k)