Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On higher-order Szego theorems with a single critical point of arbitrary
  order   We prove the following higher-order Szego theorems: if a measure on the unit
circle has absolutely continuous part $w(\theta)$ and Verblunsky coefficients
$\alpha$ with square-summable variation, then for any positive integer $m$,
$\int (1-\cos \theta)^m \log w(\theta) d\theta$ is finite if and only if
$\alpha \in \ell^{2m+2}$.
  This is the first known equivalence result of this kind in the regime of very
slow decay, i.e. with $\ell^p$ conditions with arbitrarily large $p$. The usual
difficulty of controlling higher-order sum rules is avoided by a new test
sequence approach.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th