Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Stability of Sparse Convolutions   We give a stability result for sparse convolutions on $\ell^2(G)\times
\ell^1(G)$ for torsion-free discrete Abelian groups $G$ such as $\mathbb{Z}$.
It turns out, that the torsion-free property prevents full cancellation in the
convolution of sparse sequences and hence allows to establish stability in each
entry, that is, for any fixed entry of the convolution the resulting linear map
is injective with an universal lower norm bound, which only depends on the
support cardinalities of the sequences. This can be seen as a reverse statement
of the famous Young inequality for sparse convolutions. Our result hinges on a
compression argument in additive set theory.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph