Singular spectral shift and Pushnitski $μ$-invariant

Details Singular spectral shift and Pushnitski $μ$-invariant Singular spectral shift and Pushnitski $μ$-invariant

2010-09-20

arxiv.org/abs/1009.3726v1

Mathematics

Spectral Theory

42 pages

Scientific paper

In this paper it is shown that in case of trace class perturbations the
singular part of Pushnitski $\mu$-invariant does not depend on the angle
variable. This gives an alternative proof of integer-valuedness of the singular
part of the spectral shift function. As a consequence, the Birman-Krein formula
for trace class perturbations follows.

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