2018/06/15 by Antonio G. Garcı́a, Garcia, A. G., G. Pérez-Villalón +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1806.05973
openalex publication_date 2018/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.