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Mathematical Results in Quantum Mechanics pp 59–90Cite as

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The Spectral Shift Operator

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Part of the book series: Operator Theory Advances and Applications ((OT,volume 108))

Abstract

We introduce the concept of a spectral shift operator and use it to derive Krein’s spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to Krein’s trace formula and to the Birman-Solomyak spectral averaging formula are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

    Fritz Gesztesy & Konstantin A. Makarov

  2. Department of Mathematical Physics, St. Petersburg State University, Petersburg, 198904, Russia

    Serguei N. Naboko

Authors
  1. Fritz Gesztesy
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  2. Konstantin A. Makarov
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  3. Serguei N. Naboko
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Nuclear Physics Institute Academy of Science, Rez near Prague, 25068, Czech Republic

    Jaroslav Dittrich , Pavel Exner  & Miloš Tater ,  & 

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Gesztesy, F., Makarov, K.A., Naboko, S.N. (1999). The Spectral Shift Operator. In: Dittrich, J., Exner, P., Tater, M. (eds) Mathematical Results in Quantum Mechanics. Operator Theory Advances and Applications, vol 108. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8745-8_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8745-8_5

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