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 t...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical physics, analysis, and geometry analysis, and geometry, 2013-06, Vol.16 (2), p.111-136
Main Authors: Egorova, Iryna, Michor, Johanna, Teschl, Gerald
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1385-0172
1572-9656
DOI:10.1007/s11040-012-9121-y