Invariance of a Shift-Invariant Space in Several Variables
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of ℝ, and prove the existence of shift-invariant spaces that are exa...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_16618254_v5_n4_p1031_Anastasio |
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todo:paper_16618254_v5_n4_p1031_Anastasio2023-10-03T16:28:42Z Invariance of a Shift-Invariant Space in Several Variables Anastasio, M. Cabrelli, C. Paternostro, V. Fibers Range functions Shift-invariant space Translation invariant space In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of ℝ, and prove the existence of shift-invariant spaces that are exactly invariant for each given subgroup. As an application we relate the extra invariance to the size of support of the Fourier transform of the generators of the shift-invariant space. This work extends recent results obtained for the case of one variable to several variables. © 2010 Birkhäuser Verlag Basel/Switzerland. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16618254_v5_n4_p1031_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 |
Fibers Range functions Shift-invariant space Translation invariant space |
| spellingShingle |
Fibers Range functions Shift-invariant space Translation invariant space Anastasio, M. Cabrelli, C. Paternostro, V. Invariance of a Shift-Invariant Space in Several Variables |
| topic_facet |
Fibers Range functions Shift-invariant space Translation invariant space |
| description |
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of ℝ, and prove the existence of shift-invariant spaces that are exactly invariant for each given subgroup. As an application we relate the extra invariance to the size of support of the Fourier transform of the generators of the shift-invariant space. This work extends recent results obtained for the case of one variable to several variables. © 2010 Birkhäuser Verlag Basel/Switzerland. |
| format |
JOUR |
| author |
Anastasio, M. Cabrelli, C. Paternostro, V. |
| author_facet |
Anastasio, M. Cabrelli, C. Paternostro, V. |
| author_sort |
Anastasio, M. |
| title |
Invariance of a Shift-Invariant Space in Several Variables |
| title_short |
Invariance of a Shift-Invariant Space in Several Variables |
| title_full |
Invariance of a Shift-Invariant Space in Several Variables |
| title_fullStr |
Invariance of a Shift-Invariant Space in Several Variables |
| title_full_unstemmed |
Invariance of a Shift-Invariant Space in Several Variables |
| title_sort |
invariance of a shift-invariant space in several variables |
| url |
http://hdl.handle.net/20.500.12110/paper_16618254_v5_n4_p1031_Anastasio |
| work_keys_str_mv |
AT anastasiom invarianceofashiftinvariantspaceinseveralvariables AT cabrellic invarianceofashiftinvariantspaceinseveralvariables AT paternostrov invarianceofashiftinvariantspaceinseveralvariables |
| _version_ |
1807316093908287488 |