Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct and inverse spectral problems for rank-one perturbations of
  self-adjoint operators   For a given self-adjoint operator $A$ with discrete spectrum, we completely
characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss
the inverse problem of reconstructing $B$ from its spectrum.

30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an