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arXiv · 0902.3917

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

Alice Mikikits-Leitner·Gerald Teschl
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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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Alice Mikikits-Leitner, Gerald Teschl. 2009-02-23. Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds. https://doi.org/10.1007/978-3-7643-9994-8_7

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