Shift-invariant spaces on LCA groups

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, Carlos Alberto, Paternostro, Victoria
Publicado: 2010
Materias:
Fibers
LCA groups
Range functions
Shift-invariant spaces
Translation invariant spaces
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v258_n6_p2034_Cabrelli
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 paper:paper_00221236_v258_n6_p2034_Cabrelli
record_format dspace
spelling paper:paper_00221236_v258_n6_p2034_Cabrelli2025-07-30T17:28:36Z Shift-invariant spaces on LCA groups Cabrelli, Carlos Alberto Paternostro, Victoria 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v258_n6_p2034_Cabrelli 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)
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, Carlos Alberto
Paternostro, Victoria
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.
author Cabrelli, Carlos Alberto
Paternostro, Victoria
author_facet Cabrelli, Carlos Alberto
Paternostro, Victoria
author_sort Cabrelli, Carlos Alberto
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v258_n6_p2034_Cabrelli
http://hdl.handle.net/20.500.12110/paper_00221236_v258_n6_p2034_Cabrelli
work_keys_str_mv AT cabrellicarlosalberto shiftinvariantspacesonlcagroups
AT paternostrovictoria shiftinvariantspacesonlcagroups
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