Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds

Details Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds

2009-02-23

arxiv.org/abs/0902.3917v2

Spectral Theory and Analysis, 107-124, Oper. Theory Adv. Appl. 214, 2011

Mathematics

Spectral Theory

14 pages

Scientific paper

10.1007/978-3-7643-9994-8_7

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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