Reconstruction of the Transmission Coefficient for Steplike Finite-Gap Backgrounds
Iryna Egorova, Gerald Teschl
TL;DR
This paper develops a method to reconstruct the transmission coefficient in scattering theory for one-dimensional Jacobi operators with steplike finite-gap backgrounds, extending classical formulas to more complex backgrounds.
Contribution
It introduces a generalized approach to reconstruct the transmission coefficient from minimal scattering data for steplike finite-gap backgrounds, broadening classical scattering theory.
Findings
Reconstruction of the transmission coefficient from minimal data.
Extension of the Poisson-Jensen formula to finite-gap backgrounds.
Application to steplike quasi-periodic Jacobi operators.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.