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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/126225
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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 Técnicas2025-09-29T10:02:14Zoai: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:34982025-09-29 10:02:15.26CONICET 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 |
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1844613824453279744 |
score |
13.070432 |