Article

**in Operator Theory, Analysis and Mathematical Physics, J. Janas (ed.) et al., 69-76, Oper. Theory Adv. Appl. 174, 2007**[DOI: 10.1007/978-3-7643-8135-6_6]

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

### Johanna Michor and Gerald Teschl

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.

** MSC2000:** Primary 47B36, 37K15; Secondary 81U40, 39A11

**Keywords:** *Scattering, Toda hierarchy, Trace formulas*

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