Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz bases associated with regular representations of semidirect
  product groups   This work is devoted to the study of Bessel and Riesz systems of the type
$\big\{L_{\gamma}\mathsf{f}\big\}_{\gamma\in \Gamma}$ obtained from the action
of the left regular representation $L_{\gamma}$ of a discrete non abelian group
$\Gamma$ which is a semidirect product, on a function $\mathsf{f}\in
\ell^2(\Gamma)$. The main features about these systems can be conveniently
studied by means of a simple matrix-valued function $\mathbf{F}(\xi)$. These
systems allow to derive sampling results in principal $\Gamma$-invariant
spaces, i.e., spaces obtained from the action of the group $\Gamma$ on a
element of a Hilbert space. Since the systems
$\big\{L_{\gamma}\mathsf{f}\big\}_{\gamma\in \Gamma}$ are closely related to
convolution operators, a connection with $C^*$-algebras is also established.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc