Singular spectral shift and Pushnitski $μ$-invariant

In this paper it is shown that in case of trace class perturbations the singular part of Pushnitski $μ$-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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