An operator based approach to irregular frames of translates

Autores
Balazs, Peter; Heineken, Sigrid Bettina
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider translates of functions in L 2 (Rd ) along an irregular set of points, that is, {φ(· − λk )}k∈Z—where φ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.
Fil: Balazs, Peter. Austrian Academy of Sciences; Austria
Fil: Heineken, Sigrid Bettina. 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
CANONICAL DUALS
FRAME-RELATED OPERATORS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/126225
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/126225
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An operator based approach to irregular frames of translatesBalazs, PeterHeineken, Sigrid BettinaCANONICAL DUALSFRAME-RELATED OPERATORSFRAMESIRREGULAR TRANSLATESRIESZ BASEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider translates of functions in L 2 (Rd ) along an irregular set of points, that is, {φ(· − λk )}k∈Z—where φ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.Fil: Balazs, Peter. Austrian Academy of Sciences; AustriaFil: Heineken, Sigrid Bettina. 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"; ArgentinaMultidisciplinary Digital Publishing Institute2019-05-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/126225Balazs, Peter; Heineken, Sigrid Bettina; An operator based approach to irregular frames of translates; Multidisciplinary Digital Publishing Institute; Mathematics; 7; 5; 20-5-2019; 1-112227-7390CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2227-7390/7/5/449info:eu-repo/semantics/altIdentifier/doi/10.3390/math7050449info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:31:42Zoai:ri.conicet.gov.ar:11336/126225instacron: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:34982025-10-22 11:31:42.426CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An operator based approach to irregular frames of translates
title An operator based approach to irregular frames of translates
spellingShingle An operator based approach to irregular frames of translates
Balazs, Peter
CANONICAL DUALS
FRAME-RELATED OPERATORS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
title_short An operator based approach to irregular frames of translates
title_full An operator based approach to irregular frames of translates
title_fullStr An operator based approach to irregular frames of translates
title_full_unstemmed An operator based approach to irregular frames of translates
title_sort An operator based approach to irregular frames of translates
dc.creator.none.fl_str_mv Balazs, Peter
Heineken, Sigrid Bettina
author Balazs, Peter
author_facet Balazs, Peter
Heineken, Sigrid Bettina
author_role author
author2 Heineken, Sigrid Bettina
author2_role author
dc.subject.none.fl_str_mv CANONICAL DUALS
FRAME-RELATED OPERATORS
FRAMES
IRREGULAR TRANSLATES
RIESZ BASES
topic CANONICAL DUALS
FRAME-RELATED OPERATORS
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 translates of functions in L 2 (Rd ) along an irregular set of points, that is, {φ(· − λk )}k∈Z—where φ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.
Fil: Balazs, Peter. Austrian Academy of Sciences; Austria
Fil: Heineken, Sigrid Bettina. 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 translates of functions in L 2 (Rd ) along an irregular set of points, that is, {φ(· − λk )}k∈Z—where φ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.
publishDate 2019
dc.date.none.fl_str_mv 2019-05-20
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/11336/126225
Balazs, Peter; Heineken, Sigrid Bettina; An operator based approach to irregular frames of translates; Multidisciplinary Digital Publishing Institute; Mathematics; 7; 5; 20-5-2019; 1-11
2227-7390
CONICET Digital
CONICET
url http://hdl.handle.net/11336/126225
identifier_str_mv Balazs, Peter; Heineken, Sigrid Bettina; An operator based approach to irregular frames of translates; Multidisciplinary Digital Publishing Institute; Mathematics; 7; 5; 20-5-2019; 1-11
2227-7390
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://www.mdpi.com/2227-7390/7/5/449
info:eu-repo/semantics/altIdentifier/doi/10.3390/math7050449
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
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_ 1846781923130605568
score 12.982451

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