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Trace Formulas for Jacobi Operators in Connection with Scattering Theory for Quasi-Periodic Background

J. Michor and G. Teschl

Keywords: Scattering, Toda hierarchy, Trace formulas.

Abstract: We investigate trace formulas for Jacobi 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 Toda hierarchy in this class.

MSC: Primary 47B36, 37K15; Secondary 81U40, 39A11.

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ESI Preprint 1666