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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v370_n2_p530_Anastasio_oai |
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I28-R145-paper_0022247X_v370_n2_p530_Anastasio_oai2024-08-16 Anastasio, M. Cabrelli, C. Paternostro, V. 2010 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 2010;370(2):530-537 Fiber spaces LCA groups Range functions Shift-invariant space Translation invariant space Extra invariance of shift-invariant spaces on LCA groups info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v370_n2_p530_Anastasio_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (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, M. Cabrelli, C. Paternostro, V. 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. |
| format |
Artículo Artículo publishedVersion |
| author |
Anastasio, M. Cabrelli, C. Paternostro, V. |
| author_facet |
Anastasio, M. Cabrelli, C. Paternostro, V. |
| author_sort |
Anastasio, M. |
| 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 |
http://hdl.handle.net/20.500.12110/paper_0022247X_v370_n2_p530_Anastasio https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v370_n2_p530_Anastasio_oai |
| work_keys_str_mv |
AT anastasiom extrainvarianceofshiftinvariantspacesonlcagroups AT cabrellic extrainvarianceofshiftinvariantspacesonlcagroups AT paternostrov extrainvarianceofshiftinvariantspacesonlcagroups |
| _version_ |
1809357072670654464 |