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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Autores principales: Anastasio, Magalí, Cabrelli, Carlos Alberto, Paternostro, Victoria
Publicado: 2011
Materias:
Fibers
Range functions
Shift-invariant space
Translation invariant space
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618254_v5_n4_p1031_Anastasio
http://hdl.handle.net/20.500.12110/paper_16618254_v5_n4_p1031_Anastasio
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_16618254_v5_n4_p1031_Anastasio
record_format dspace
spelling paper:paper_16618254_v5_n4_p1031_Anastasio2023-06-08T16:25:44Z Invariance of a Shift-Invariant Space in Several Variables Anastasio, Magalí Cabrelli, Carlos Alberto Paternostro, Victoria 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618254_v5_n4_p1031_Anastasio 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, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
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.
author Anastasio, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
author_facet Anastasio, Magalí
Cabrelli, Carlos Alberto
Paternostro, Victoria
author_sort Anastasio, Magalí
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
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618254_v5_n4_p1031_Anastasio
http://hdl.handle.net/20.500.12110/paper_16618254_v5_n4_p1031_Anastasio
work_keys_str_mv AT anastasiomagali invarianceofashiftinvariantspaceinseveralvariables
AT cabrellicarlosalberto invarianceofashiftinvariantspaceinseveralvariables
AT paternostrovictoria invarianceofashiftinvariantspaceinseveralvariables
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