Global symmetric approximation of frames

Autores
Chiumiento, Eduardo Hernan
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
SYMMETRIC APPROXIMATION
FRAME
HILBERT SPACE
HILBERT SCHMIDT OPERATORS
INDEX OF A PAIR OF PROJECTIONS
PARTIAL ISOMETRY
LÖWDIN ORTHOGONALIZATION
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:11336/108156
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/108156
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Global symmetric approximation of framesChiumiento, Eduardo HernanSYMMETRIC APPROXIMATIONFRAMEHILBERT SPACEHILBERT SCHMIDT OPERATORSINDEX OF A PAIR OF PROJECTIONSPARTIAL ISOMETRYLÖWDIN ORTHOGONALIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSpringer2019-08info: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/11336/108156Chiumiento, Eduardo Hernan; Global symmetric approximation of frames; Springer; Journal Of Fourier Analysis And Applications; 25; 4; 8-2019; 1395-14231069-5869CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-018-9632-4info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-018-9632-4info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.08543info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:37:21Zoai:ri.conicet.gov.ar:11336/108156instacron: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 09:37:21.6CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global symmetric approximation of frames
title Global symmetric approximation of frames
spellingShingle Global symmetric approximation of frames
Chiumiento, Eduardo Hernan
SYMMETRIC APPROXIMATION
FRAME
HILBERT SPACE
HILBERT SCHMIDT OPERATORS
INDEX OF A PAIR OF PROJECTIONS
PARTIAL ISOMETRY
LÖWDIN ORTHOGONALIZATION
title_short Global symmetric approximation of frames
title_full Global symmetric approximation of frames
title_fullStr Global symmetric approximation of frames
title_full_unstemmed Global symmetric approximation of frames
title_sort Global symmetric approximation of frames
dc.creator.none.fl_str_mv Chiumiento, Eduardo Hernan
author Chiumiento, Eduardo Hernan
author_facet Chiumiento, Eduardo Hernan
author_role author
dc.subject.none.fl_str_mv SYMMETRIC APPROXIMATION
FRAME
HILBERT SPACE
HILBERT SCHMIDT OPERATORS
INDEX OF A PAIR OF PROJECTIONS
PARTIAL ISOMETRY
LÖWDIN ORTHOGONALIZATION
topic SYMMETRIC APPROXIMATION
FRAME
HILBERT SPACE
HILBERT SCHMIDT OPERATORS
INDEX OF A PAIR OF PROJECTIONS
PARTIAL ISOMETRY
LÖWDIN ORTHOGONALIZATION
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 solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.
publishDate 2019
dc.date.none.fl_str_mv 2019-08
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/11336/108156
Chiumiento, Eduardo Hernan; Global symmetric approximation of frames; Springer; Journal Of Fourier Analysis And Applications; 25; 4; 8-2019; 1395-1423
1069-5869
CONICET Digital
CONICET
url http://hdl.handle.net/11336/108156
identifier_str_mv Chiumiento, Eduardo Hernan; Global symmetric approximation of frames; Springer; Journal Of Fourier Analysis And Applications; 25; 4; 8-2019; 1395-1423
1069-5869
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://link.springer.com/article/10.1007/s00041-018-9632-4
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-018-9632-4
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.08543
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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