Riesz bases associated with regular representations of semidirect product groups

Abstract

This work is devoted to the study of Bessel and Riesz systems of the type Lγ f γ ∈ obtained from the action of the left regular representation Lγ of a discrete non abelian group which is a semidirect product, on a function f ∈ 2(). The main features about these systems can be conveniently studied by means of a simple matrix-valued function F(ξ ). These systems allow to derive sampling results in principal -invariant spaces, i.e., spaces obtained from the action of the group on a element of a Hilbert space. Since the systems Lγ f γ ∈ are closely related to convolution operators, a connection with C∗-algebras is also established.