09-35 Alice Mikikits-Leitner and Gerald Teschl

Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds (43K, LaTeX2e) Feb 23, 09

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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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