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

作者：Egorova Iryna; Michor Johanna; Teschl Gerald^*

来源：Mathematical Physics, Analysis and Geometry, 2013, 16(2): 111-136.

DOI：10.1007/s11040-012-9121-y

• Inverse scattering
• Jacobi operators
• Finite-gap
• Steplike

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.

• 出版日期2013-6