Invariance of a shift-invariant space

Autores
Aldroubi, Akram; Cabrelli, Carlos; Heil, Christopher; Kornelson, Keri; Molter, Ursula Maria
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.
Fil: Aldroubi, Akram. Vanderbilt University; Estados Unidos
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Heil, Christopher. Georgia Institute of Techology; Estados Unidos
Fil: Kornelson, Keri. University of Oklahoma; Estados Unidos
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DIMENSION FUNCTION
FIBER SPACE
FRAMES
GRAMIAN OPERATOR
RANGE FUNCTION
RIESZ BASIS
SHIFT-INVARIANT SPACE
TRANSLATION-INVARIANT SPACE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/69116
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/69116
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Invariance of a shift-invariant spaceAldroubi, AkramCabrelli, CarlosHeil, ChristopherKornelson, KeriMolter, Ursula MariaDIMENSION FUNCTIONFIBER SPACEFRAMESGRAMIAN OPERATORRANGE FUNCTIONRIESZ BASISSHIFT-INVARIANT SPACETRANSLATION-INVARIANT SPACEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.Fil: Aldroubi, Akram. Vanderbilt University; Estados UnidosFil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Heil, Christopher. Georgia Institute of Techology; Estados UnidosFil: Kornelson, Keri. University of Oklahoma; Estados UnidosFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaBirkhauser Boston Inc2010-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/69116Aldroubi, Akram; Cabrelli, Carlos; Heil, Christopher; Kornelson, Keri; Molter, Ursula Maria; Invariance of a shift-invariant space; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 16; 1; 1-2010; 60-751069-58691531-5851CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0804.1597info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-009-9068-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-009-9068-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:23:00Zoai:ri.conicet.gov.ar:11336/69116instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:23:00.718CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Invariance of a shift-invariant space
title Invariance of a shift-invariant space
spellingShingle Invariance of a shift-invariant space
Aldroubi, Akram
DIMENSION FUNCTION
FIBER SPACE
FRAMES
GRAMIAN OPERATOR
RANGE FUNCTION
RIESZ BASIS
SHIFT-INVARIANT SPACE
TRANSLATION-INVARIANT SPACE
title_short Invariance of a shift-invariant space
title_full Invariance of a shift-invariant space
title_fullStr Invariance of a shift-invariant space
title_full_unstemmed Invariance of a shift-invariant space
title_sort Invariance of a shift-invariant space
dc.creator.none.fl_str_mv Aldroubi, Akram
Cabrelli, Carlos
Heil, Christopher
Kornelson, Keri
Molter, Ursula Maria
author Aldroubi, Akram
author_facet Aldroubi, Akram
Cabrelli, Carlos
Heil, Christopher
Kornelson, Keri
Molter, Ursula Maria
author_role author
author2 Cabrelli, Carlos
Heil, Christopher
Kornelson, Keri
Molter, Ursula Maria
author2_role author
author
author
author
dc.subject.none.fl_str_mv DIMENSION FUNCTION
FIBER SPACE
FRAMES
GRAMIAN OPERATOR
RANGE FUNCTION
RIESZ BASIS
SHIFT-INVARIANT SPACE
TRANSLATION-INVARIANT SPACE
topic DIMENSION FUNCTION
FIBER SPACE
FRAMES
GRAMIAN OPERATOR
RANGE FUNCTION
RIESZ BASIS
SHIFT-INVARIANT SPACE
TRANSLATION-INVARIANT SPACE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.
Fil: Aldroubi, Akram. Vanderbilt University; Estados Unidos
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Heil, Christopher. Georgia Institute of Techology; Estados Unidos
Fil: Kornelson, Keri. University of Oklahoma; Estados Unidos
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.
publishDate 2010
dc.date.none.fl_str_mv 2010-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/69116
Aldroubi, Akram; Cabrelli, Carlos; Heil, Christopher; Kornelson, Keri; Molter, Ursula Maria; Invariance of a shift-invariant space; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 16; 1; 1-2010; 60-75
1069-5869
1531-5851
CONICET Digital
CONICET
url http://hdl.handle.net/11336/69116
identifier_str_mv Aldroubi, Akram; Cabrelli, Carlos; Heil, Christopher; Kornelson, Keri; Molter, Ursula Maria; Invariance of a shift-invariant space; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 16; 1; 1-2010; 60-75
1069-5869
1531-5851
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0804.1597
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-009-9068-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-009-9068-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842981268162084864
score 12.48226

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