Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Wiener's lemma for locally compact abelian groups   Inspired by an extension of Wiener's lemma on the relation of measures $\mu$
on the unit circle and their Fourier coefficients $\widehat{\mu}(k_n)$ along
subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19,
arXiv:1701.00101], we study the validity of the lemma when the Fourier
coefficients are weighted by a sequence of probability measures. By using
convergence with respect to a filter derived from these measure sequences, we
obtain similar results, now also allowing the consideration of locally compact
abelian groups other than $\mathbb{T}$ and $\mathbb{R}$. As an application, we
present an extension of a result of Goldstein [Gol96] on the action of
semigroups on Hilbert spaces.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int