Time–frequency shift invariance and the Amalgam Balian–Low theorem

Autores
Cabrelli, Carlos; Molter, Ursula Maria; Pfander, Götz E.
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
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: 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
Fil: Pfander, Götz E.. Universitat Bremen. School of Enigineerring and Science Jacobs; Alemania
Materia
Balian Low Theorem
Addicional Shift Invariance
Gabor Frames
Time Frequence Analysis
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:11336/55542
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55542
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Time–frequency shift invariance and the Amalgam Balian–Low theoremCabrelli, CarlosMolter, Ursula MariaPfander, Götz E.Balian Low TheoremAddicional Shift InvarianceGabor FramesTime Frequence Analysishttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.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"; ArgentinaFil: 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"; ArgentinaFil: Pfander, Götz E.. Universitat Bremen. School of Enigineerring and Science Jacobs; AlemaniaAcademic Press Inc Elsevier Science2016-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55542Cabrelli, Carlos; Molter, Ursula Maria; Pfander, Götz E.; Time–frequency shift invariance and the Amalgam Balian–Low theorem; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 41; 3; 11-2016; 677-6911063-5203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520315000524info:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2015.04.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:15:59Zoai:ri.conicet.gov.ar:11336/55542instacron: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:34982025-10-15 15:15:59.822CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Time–frequency shift invariance and the Amalgam Balian–Low theorem
title Time–frequency shift invariance and the Amalgam Balian–Low theorem
spellingShingle Time–frequency shift invariance and the Amalgam Balian–Low theorem
Cabrelli, Carlos
Balian Low Theorem
Addicional Shift Invariance
Gabor Frames
Time Frequence Analysis
title_short Time–frequency shift invariance and the Amalgam Balian–Low theorem
title_full Time–frequency shift invariance and the Amalgam Balian–Low theorem
title_fullStr Time–frequency shift invariance and the Amalgam Balian–Low theorem
title_full_unstemmed Time–frequency shift invariance and the Amalgam Balian–Low theorem
title_sort Time–frequency shift invariance and the Amalgam Balian–Low theorem
dc.creator.none.fl_str_mv Cabrelli, Carlos
Molter, Ursula Maria
Pfander, Götz E.
author Cabrelli, Carlos
author_facet Cabrelli, Carlos
Molter, Ursula Maria
Pfander, Götz E.
author_role author
author2 Molter, Ursula Maria
Pfander, Götz E.
author2_role author
author
dc.subject.none.fl_str_mv Balian Low Theorem
Addicional Shift Invariance
Gabor Frames
Time Frequence Analysis
topic Balian Low Theorem
Addicional Shift Invariance
Gabor Frames
Time Frequence Analysis
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
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: 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
Fil: Pfander, Götz E.. Universitat Bremen. School of Enigineerring and Science Jacobs; Alemania
description We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
publishDate 2016
dc.date.none.fl_str_mv 2016-11
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/11336/55542
Cabrelli, Carlos; Molter, Ursula Maria; Pfander, Götz E.; Time–frequency shift invariance and the Amalgam Balian–Low theorem; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 41; 3; 11-2016; 677-691
1063-5203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55542
identifier_str_mv Cabrelli, Carlos; Molter, Ursula Maria; Pfander, Götz E.; Time–frequency shift invariance and the Amalgam Balian–Low theorem; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 41; 3; 11-2016; 677-691
1063-5203
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520315000524
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2015.04.003
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
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score 13.22299

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