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

publication date

  • January 2020

start page

  • 41

end page

  • 62

volume

  • 14

International Standard Serial Number (ISSN)

  • 1735-8787

abstract

  • This work is devoted to the study of Bessel and Riesz systems of the type {Lgammaf}gamma∈Gamma obtained from the action of the left regular representation Lgamma of a discrete non abelian group Gamma which is a semidirect product, on a function f∈ℓ2(Gamma). The main features about these systems can be conveniently studied by means of a simple matrix-valued function 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 {Lgammaf}gamma∈Gamma are closely related to convolution operators, a connection with C∗-algebras is also established

keywords

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