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 {Lγf}γ∈Γ obtained from the action of the left regular representation Lγ of a discrete non abelian group Γ which is a semidirect product, on a function f∈ℓ2(Γ). 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 Γ-invariant spaces, i.e., spaces obtained from the action of the group Γ on a element of a Hilbert space. Since the systems {Lγf}γ∈Γ are closely related to convolution operators, a connection with C∗-algebras is also established.

semidirect product of groups; left regular representation of a group; dual riesz bases and sampling expansions

Riesz bases associated with regular representations of semidirect product groups Articles