Sampling theory, oblique projections and a question by Smale and Zhou

In a recent article, Smale and Zhou define a notion of rich data for sampling problems and reconstruction of signals from a discrete set of samples and study different least-square problems related with the minimization of the error. They obtain different error estimations assuming that the original...

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Detalles Bibliográficos
Autores: Antezana, Jorge Abel, Corach, Gustavo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/98217
Acceso en línea:http://hdl.handle.net/11336/98217
Access Level:acceso abierto
Palabra clave:ANGLES AND COMPATIBILITY
FRAMES
OBLIQUE PROJECTION
SAMPLING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Sampling theory, oblique projections and a question by Smale and ZhouAntezana, Jorge AbelCorach, GustavoANGLES AND COMPATIBILITYFRAMESOBLIQUE PROJECTIONSAMPLINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In a recent article, Smale and Zhou define a notion of rich data for sampling problems and reconstruction of signals from a discrete set of samples and study different least-square problems related with the minimization of the error. They obtain different error estimations assuming that the original signal belong to the reconstruction subspace and they propose to find error estimations if this assumption does not hold. In this paper, using projection methods, we find such estimates and we extend from reproducing kernel Hilbert spaces to abstract Hilbert spaces some of their results on function reconstruction from point values.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2006-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98217Antezana, Jorge Abel; Corach, Gustavo; Sampling theory, oblique projections and a question by Smale and Zhou; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 21; 2; 9-2006; 245-2531063-5203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2006.01.001info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520306000030info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:41:01Zoai:ri.conicet.gov.ar:11336/98217instacron: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:34982024-05-08 13:41:01.926CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sampling theory, oblique projections and a question by Smale and Zhou
title Sampling theory, oblique projections and a question by Smale and Zhou
spellingShingle Sampling theory, oblique projections and a question by Smale and Zhou
Antezana, Jorge Abel
ANGLES AND COMPATIBILITY
FRAMES
OBLIQUE PROJECTION
SAMPLING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Sampling theory, oblique projections and a question by Smale and Zhou
title_full Sampling theory, oblique projections and a question by Smale and Zhou
title_fullStr Sampling theory, oblique projections and a question by Smale and Zhou
title_full_unstemmed Sampling theory, oblique projections and a question by Smale and Zhou
title_sort Sampling theory, oblique projections and a question by Smale and Zhou
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Corach, Gustavo
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Corach, Gustavo
author_role author
author2 Corach, Gustavo
author2_role author
dc.subject.none.fl_str_mv ANGLES AND COMPATIBILITY
FRAMES
OBLIQUE PROJECTION
SAMPLING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic ANGLES AND COMPATIBILITY
FRAMES
OBLIQUE PROJECTION
SAMPLING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In a recent article, Smale and Zhou define a notion of rich data for sampling problems and reconstruction of signals from a discrete set of samples and study different least-square problems related with the minimization of the error. They obtain different error estimations assuming that the original signal belong to the reconstruction subspace and they propose to find error estimations if this assumption does not hold. In this paper, using projection methods, we find such estimates and we extend from reproducing kernel Hilbert spaces to abstract Hilbert spaces some of their results on function reconstruction from point values.
publishDate 2006
dc.date.none.fl_str_mv 2006-09
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/11336/98217
Antezana, Jorge Abel; Corach, Gustavo; Sampling theory, oblique projections and a question by Smale and Zhou; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 21; 2; 9-2006; 245-253
1063-5203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98217
identifier_str_mv Antezana, Jorge Abel; Corach, Gustavo; Sampling theory, oblique projections and a question by Smale and Zhou; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 21; 2; 9-2006; 245-253
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/10.1016/j.acha.2006.01.001
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1063520306000030
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
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.812429

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