Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Krein spectral shift and rank one perturbations of spectra   We use recent results on the boundary behavior of Cauchy integrals to study
the Krein spectral shift of a rank one perturbation problem for self-adjoint
operators. As an application, we prove that all self-adjoint rank one
perturbations of a self-adjoint operator are pure point if and only if the
spectrum of the operator is countable. We also study pairs of pure point
operators unitarily equivalent up to a rank one perturbation and give various
examples of rank one perturbations of singular spectra.

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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: dg-ga