Mathematical Physics, Analysis and Geometry

, Volume 16, Issue 2, pp 111–136 | Cite as

Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data



We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.


Inverse scattering Jacobi operators Finite-gap Steplike 

Mathematics Subject Classifications (2010)

Primary 47B36 81U40; Secondary 34L25 39A10 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Iryna Egorova
    • 1
  • Johanna Michor
    • 2
    • 3
  • Gerald Teschl
    • 2
    • 3
  1. 1.Institute for Low Temperature PhysicsKharkivUkraine
  2. 2.Faculty of MathematicsUniversity of ViennaWienAustria
  3. 3.International Erwin Schrödinger Institute for Mathematical PhysicsWienAustria

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