Riesz bases associated with regular representations of semidirect product groups (Q2287438)

In this research, the authors deal on characterizing some systems of the type \(\{L_{\gamma} f\}_{\gamma\in \Gamma}\) obtained from the left regular representation of a discrete non-ablelian group \(\Gamma\) and \(f\in \ell^{2}(\Gamma)\). Basically, the results include conditions under which the systems are a Riesz basis or a Bessel sequence. They are achieved by using matrix language analysis and convenient matrices. The applied matrices are somehow related to the Zak-transform. The authors study some applications on sampling theory. In addition, they provide various results on this topic relating to \(C^\ast\)-algebras. In my view the paper touched an interesting problem in representation theory and the results sound correct. The manuscript is well-organized and well-written. In addition, it seems to be relevant in some areas related to quantum theory and it can be examined on some other groups.