Riesz bases associated with regular representations of semidirect product groups Articles uri icon

publication date

  • December 2019

start page

  • 41

end page

  • 62


  • 1


  • 14

International Standard Serial Number (ISSN)

  • 1735-8787


  • 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.


  • Mathematics


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