Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criterion of holomorphy with respect to a coupling constant of
  continuous functions of a perturbed self-adjoint operator   Sufficient and necessary conditions on the spectral measure of a self-adjoint
operator $A$, acting in a Hilbert space, are obtained, under which for any
continuous scalar function the operator function $\phi(A+\gamma B)$ is
holomorphic with rspect to the coupling constant $\gamma$ in a neighborhood of
$\gamma=0$, where $B$ is a self-adjoint operator. The sharpest results are
obtained in the case where $B$ is a rank-one operator.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics