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Riesz bases associated with regular representations of semidirect product groups

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2019-12
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Springer Science and Business Media LLC
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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.
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Semidirect product of groups, Left regular representation of a group, Dual riesz bases and sampling expansions
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García, A. G., & Pérez-Villalón, G. (2019). Riesz bases associated with regular representations of semidirect product groups. In Banach Journal of Mathematical Analysis, 14(1), 41–62