The Spectral Shift Operator

Fritz Gesztesy; Konstantin A. Makarov; Serguei N. Naboko

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The Spectral Shift Operator

Fritz Gesztesy·Konstantin A. Makarov·Serguei N. Naboko

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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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BibTeX RIS

Fritz Gesztesy, Konstantin A. Makarov, Serguei N. Naboko. 1999-01-26. The Spectral Shift Operator. https://arxiv.org/abs/math/9901112

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