Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications

Autores
Heineken, Sigrid Bettina; Matusiak, Ewa; Paternostro, Victoria
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces.
Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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: Matusiak Ewa. Universidad de Viena; Austria
Fil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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
APPROXIMATE RECONSTRUCTIONS
BANDLIMITED FUNCTIONS
CANONICAL DUALS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/93867
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applicationsHeineken, Sigrid BettinaMatusiak, EwaPaternostro, VictoriaAPPROXIMATE RECONSTRUCTIONSBANDLIMITED FUNCTIONSCANONICAL DUALSFRAMESIRREGULAR TRANSLATESRIESZ BASEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces.Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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: Matusiak Ewa. Universidad de Viena; AustriaFil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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"; ArgentinaWorld Scientific2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93867Heineken, Sigrid Bettina; Matusiak, Ewa; Paternostro, Victoria; Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications; World Scientific; International Journal of Wavelets, Multiresolution and Information Processing; 12; 2; 3-2014; 1-17; 14500190219-6913CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0219691314500192info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0219691314500192info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:45:32Zoai:ri.conicet.gov.ar:11336/93867instacron: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:34982025-09-29 09:45:32.736CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
spellingShingle Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
Heineken, Sigrid Bettina
APPROXIMATE RECONSTRUCTIONS
BANDLIMITED FUNCTIONS
CANONICAL DUALS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
title_short Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_full Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_fullStr Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_full_unstemmed Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_sort Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
dc.creator.none.fl_str_mv Heineken, Sigrid Bettina
Matusiak, Ewa
Paternostro, Victoria
author Heineken, Sigrid Bettina
author_facet Heineken, Sigrid Bettina
Matusiak, Ewa
Paternostro, Victoria
author_role author
author2 Matusiak, Ewa
Paternostro, Victoria
author2_role author
author
dc.subject.none.fl_str_mv APPROXIMATE RECONSTRUCTIONS
BANDLIMITED FUNCTIONS
CANONICAL DUALS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
topic APPROXIMATE RECONSTRUCTIONS
BANDLIMITED FUNCTIONS
CANONICAL DUALS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
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 perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces.
Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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: Matusiak Ewa. Universidad de Viena; Austria
Fil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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 We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/93867
Heineken, Sigrid Bettina; Matusiak, Ewa; Paternostro, Victoria; Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications; World Scientific; International Journal of Wavelets, Multiresolution and Information Processing; 12; 2; 3-2014; 1-17; 1450019
0219-6913
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93867
identifier_str_mv Heineken, Sigrid Bettina; Matusiak, Ewa; Paternostro, Victoria; Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications; World Scientific; International Journal of Wavelets, Multiresolution and Information Processing; 12; 2; 3-2014; 1-17; 1450019
0219-6913
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219691314500192
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0219691314500192
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
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 13.070432

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