Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Operator theoretic approach to the convergence of rearranged Fourier
  series   This article studies the rearrangement problem for Fourier series introduced
by P.L. Ulyanov, who conjectured that every continuous function on the torus
admits a rearrangement of its Fourier coefficients such that the rearranged
partial sums of the Fourier series converge uniformly to the function. The main
theorem here gives several new equivalences to this conjecture in terms of the
convergence of the rearranged Fourier series in the strong (equivalently in
this case, weak) operator topologies on $B(L_2(T))$. Additionally, a new
framework for further investigation is introduced by considering convergence
for subspaces of $L_2$, which leads to many methods for attempting to prove or
disprove Ulyanov's conjecture. In this framework, we provide characterizations
of unconditional convergence of the Fourier series in the SOT and WOT. These
considerations also give rise to some interesting questions regarding weaker
versions of the rearrangement problem.
  Along the way, we consider some interesting questions related to the
classical theory of trigonometric polynomials. All of the results here admit
natural extensions to arbitrary dimensions.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th