Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds
Spectral Theory
2012-04-03 v2 Mathematical Physics
math.MP
Abstract
We investigate trace formulas for one-dimensional Schroedinger operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular, we establish the conserved quantities for the solutions of the Korteweg-de Vries hierarchy in this class and relate them to the reflection coefficients via Abelian integrals on the underlying hyperelliptic Riemann surface.
Keywords
Cite
@article{arxiv.0902.3917,
title = {Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds},
author = {Alice Mikikits-Leitner and Gerald Teschl},
journal= {arXiv preprint arXiv:0902.3917},
year = {2012}
}
Comments
14 pages