Shift-invariant spaces on LCA groups

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In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. A...

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Autores principales: Cabrelli, C., Paternostro, V.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Materias:
Fibers
LCA groups
Range functions
Shift-invariant spaces
Translation invariant spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00221236_v258_n6_p2034_Cabrelli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_00221236_v258_n6_p2034_Cabrelli
record_format dspace
spelling paperaa:paper_00221236_v258_n6_p2034_Cabrelli2023-06-12T16:43:51Z Shift-invariant spaces on LCA groups J. Funct. Anal. 2010;258(6):2034-2059 Cabrelli, C. Paternostro, V. Fibers LCA groups Range functions Shift-invariant spaces Translation invariant spaces In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd. © 2009 Elsevier Inc. All rights reserved. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v258_n6_p2034_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Fibers
LCA groups
Range functions
Shift-invariant spaces
Translation invariant spaces
spellingShingle Fibers
LCA groups
Range functions
Shift-invariant spaces
Translation invariant spaces
Cabrelli, C.
Paternostro, V.
Shift-invariant spaces on LCA groups
topic_facet Fibers
LCA groups
Range functions
Shift-invariant spaces
Translation invariant spaces
description In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd. © 2009 Elsevier Inc. All rights reserved.
format Artículo
Artículo
publishedVersion
author Cabrelli, C.
Paternostro, V.
author_facet Cabrelli, C.
Paternostro, V.
author_sort Cabrelli, C.
title Shift-invariant spaces on LCA groups
title_short Shift-invariant spaces on LCA groups
title_full Shift-invariant spaces on LCA groups
title_fullStr Shift-invariant spaces on LCA groups
title_full_unstemmed Shift-invariant spaces on LCA groups
title_sort shift-invariant spaces on lca groups
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_00221236_v258_n6_p2034_Cabrelli
work_keys_str_mv AT cabrellic shiftinvariantspacesonlcagroups
AT paternostrov shiftinvariantspacesonlcagroups
_version_ 1769810164502757376

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