Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity of spectral averaging   We consider averages $\kappa$ of spectral measures of rank one perturbations
with respect to a $\sigma$-finite measure $\nu$. It is examined how various
degrees of continuity of $\nu$ with respect to $\alpha$-dimensional Hausdorff
measures ($0 \leq \alpha \leq 1$) are inherited by $\kappa$. This extends
Kotani's trick where $\nu$ is simply the Lebesgue measure.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an