Riesz and frame systems generated by unitary actions of discrete groups
Entidad
UAM. Departamento de MatemáticasEditor
ElsevierFecha de edición
2015-11-01Cita
10.1016/j.acha.2014.09.007
Applied and Computational Harmonic Analysis 39.3 (2015): 369-399
ISSN
1063-5203 (print); 1096-603X (online)DOI
10.1016/j.acha.2014.09.007Versión del editor
http://dx.doi.org/10.1016/j.acha.2014.09.007Materias
Frames; Group theory; Group von Neumann algebras; Noncommutative harmonic analysis; Riesz bases; Shift-invariant spaces; MatemáticasNota
This is the peer reviewed version of the following article: Applied and Computational Harmonic Analysis 39.3 (2015): 369-399, which has been published in final form at http://dx.doi.org/10.1016/j.acha.2014.09.007Derechos
© 2014 Elsevier Inc.Resumen
We characterize orthonormal bases, Riesz bases and frames which arise from the action of a countable discrete group Γ on a single element ψ of a given Hilbert space H. As Γ might not be abelian, this is done in terms of a bracket map taking values in the L1-space associated to the group von Neumann algebra of Γ. Our result generalizes recent work for LCA groups in [26]. In many cases, the bracket map can be computed in terms of a noncommutative form of the Zak transform
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Google Scholar:Barbieri, Davide
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Hernández Rodríguez, Eugenio
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Parcet, Javier
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