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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.

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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}
}

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14 pages