Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pushnitski's $\mu$-invariant and Schr\"odinger operators with embedded
  eigenvalues   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.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat