The Spectral Shift Operator

Details The Spectral Shift Operator The Spectral Shift Operator

1999-01-26

arxiv.org/abs/math/9901112v1

Mathematics

Spectral Theory

LaTeX, 28 pages

Scientific paper

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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