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

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Operator Theory, Analysis and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 174))

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.

Work supported by the Austrian Science Fund (FWF) under Grant No. P17762.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Nordbergstrasse 15, A-1090, Wien, Austria

    Johanna Michor & Gerald Teschl

  2. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Wien, Austria

    Johanna Michor & Gerald Teschl

Authors
  1. Johanna Michor
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  2. Gerald Teschl
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Dept. of Mathematics, Imperial College London, Room 675 South Kensington Campus, SW7 2AZ, London, UK

    Ari Laptev

  4. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  5. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    Günter Stolz

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Michor, J., Teschl, G. (2007). Trace Formulas for Jacobi Operators in Connection with Scattering Theory for Quasi-Periodic Background. In: Janas, J., Kurasov, P., Laptev, A., Naboko, S., Stolz, G. (eds) Operator Theory, Analysis and Mathematical Physics. Operator Theory: Advances and Applications, vol 174. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8135-6_6

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