Pushnitski's $μ$-invariant and Schrödinger operators with embedded eigenvalues

Details Pushnitski's $μ$-invariant and Schrödinger operators with embedded eigenvalues Pushnitski's $μ$-invariant and Schrödinger operators with embedded eigenvalues

2007-11-08

arxiv.org/abs/0711.1190v1

Mathematics

Spectral Theory

LaTeX, 9 pages

Scientific paper

In this note, under a certain assumption on an affine space of operators, which admit embedded eigenvalues, it is shown that the singular part of the spectral shift function of any pair of operators from this space is an integer-valued function. The proof uses a natural decomposition of Pushnitski's $\mu$-invariant into "absolutely continuous" and "singular" parts. As a corollary, the Birman-Krein formula follows.

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