The Spectral Shift Operator
Spectral Theory
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9901112,
title = {The Spectral Shift Operator},
author = {Fritz Gesztesy and Konstantin A. Makarov and Serguei N. Naboko},
journal= {arXiv preprint arXiv:math/9901112},
year = {2007}
}
Comments
LaTeX, 28 pages