Extra invariance of shift-invariant spaces on LCA groups

This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of...

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Autores principales: Anastasio, Magalí, Cabrelli, Carlos Alberto, Paternostro, Victoria
Publicado: 2010
Materias:
Fiber spaces
LCA groups
Range functions
Shift-invariant space
Translation invariant space
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v370_n2_p530_Anastasio
http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v370_n2_p530_Anastasio
record_format dspace
spelling paper:paper_0022247X_v370_n2_p530_Anastasio2025-07-30T17:30:01Z Extra invariance of shift-invariant spaces on LCA groups Anastasio, Magalí Cabrelli, Carlos Alberto Paternostro, Victoria Fiber spaces LCA groups Range functions Shift-invariant space Translation invariant space This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M' containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance. © 2010 Elsevier Inc. Fil:Anastasio, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 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_0022247X_v370_n2_p530_Anastasio http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fiber spaces
LCA groups
Range functions
Shift-invariant space
Translation invariant space
spellingShingle Fiber spaces
LCA groups
Range functions
Shift-invariant space
Translation invariant space
Anastasio, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
Extra invariance of shift-invariant spaces on LCA groups
topic_facet Fiber spaces
LCA groups
Range functions
Shift-invariant space
Translation invariant space
description This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M' containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance. © 2010 Elsevier Inc.
author Anastasio, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
author_facet Anastasio, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
author_sort Anastasio, Magalí
title Extra invariance of shift-invariant spaces on LCA groups
title_short Extra invariance of shift-invariant spaces on LCA groups
title_full Extra invariance of shift-invariant spaces on LCA groups
title_fullStr Extra invariance of shift-invariant spaces on LCA groups
title_full_unstemmed Extra invariance of shift-invariant spaces on LCA groups
title_sort extra invariance of shift-invariant spaces on lca groups
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v370_n2_p530_Anastasio
http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio
work_keys_str_mv AT anastasiomagali extrainvarianceofshiftinvariantspacesonlcagroups
AT cabrellicarlosalberto extrainvarianceofshiftinvariantspacesonlcagroups
AT paternostrovictoria extrainvarianceofshiftinvariantspacesonlcagroups
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