Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory

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Show simple item record García García, Antonio Hernández Medina, Miguel Ángel Pérez Villalón, Gerardo 2021-04-23T11:40:04Z 2021-04-23T11:40:04Z 2020-02-05
dc.identifier.bibliographicCitation Results in Mathematics, (2020), v. 75, Article number: 40.
dc.identifier.issn 1422-6383
dc.description.abstract A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space H is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group G on H. The samples are defined by means of a filtering process which generalizes the usual sampling settings. The multiply generated setting allows to consider some examples where the group G is non-abelian as, for instance, crystallographic groups. Finally, it is worth to mention that classical average or pointwise sampling in shift-invariant subspaces are particular examples included in the followed approach.
dc.description.sponsorship This work has been supported by the grant MTM2017-84098-P from the Spanish Ministerio de Economía y Competitividad (MINECO).
dc.format.extent 22
dc.language.iso eng
dc.publisher Springer
dc.rights © 2020 Springer Nature Switzerland AG.
dc.subject.other Convolution systems
dc.subject.other Discrete abelian groups
dc.subject.other Dual frames
dc.subject.other Sampling expansion
dc.subject.other Unitary representation of a group
dc.title Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2017-84098-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationlastpage 22
dc.identifier.publicationtitle Results in Mathematics
dc.identifier.publicationvolume 75
dc.identifier.uxxi AR/0000025589
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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