Tight frame completions with prescribed norms

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be a finite dimensional (real or complex) Hilbert space and let {a_i} ∞_i=1. be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {f_i}p_i=1 in H we find necessary and sufficient conditions for the existence of r ∈ N U {∞} and a Bessel sequence G = {g_i}r_i=1  in H such that F U G is a tight frame for H and || g_i ||^2 = a_i for every i. Moreover, in this case we compute the minimum r in NU {∞} with this property. We also describe algorithms that perform completions of a given set of vectors to tight frames.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Materia
FRAME
TIGHT FRAME COMPLETIONS
MAJORIZATION
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:11336/110304
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/110304
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Tight frame completions with prescribed normsMassey, Pedro GustavoRuiz, Mariano AndresFRAMETIGHT FRAME COMPLETIONSMAJORIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a finite dimensional (real or complex) Hilbert space and let {a_i} ∞_i=1. be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {f_i}p_i=1 in H we find necessary and sufficient conditions for the existence of r ∈ N U {∞} and a Bessel sequence G = {g_i}r_i=1  in H such that F U G is a tight frame for H and || g_i ||^2 = a_i for every i. Moreover, in this case we compute the minimum r in NU {∞} with this property. We also describe algorithms that perform completions of a given set of vectors to tight frames.Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaSampling Publishing2008-01info: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/11336/110304Massey, Pedro Gustavo; Ruiz, Mariano Andres; Tight frame completions with prescribed norms; Sampling Publishing ; Sampling Theory in Signal and Image Processing; 7; 1; 1-2008; 1-131530-6429CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://stsip.org/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:20:56Zoai:ri.conicet.gov.ar:11336/110304instacron: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:34982025-09-10 13:20:57.102CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Tight frame completions with prescribed norms
title Tight frame completions with prescribed norms
spellingShingle Tight frame completions with prescribed norms
Massey, Pedro Gustavo
FRAME
TIGHT FRAME COMPLETIONS
MAJORIZATION
title_short Tight frame completions with prescribed norms
title_full Tight frame completions with prescribed norms
title_fullStr Tight frame completions with prescribed norms
title_full_unstemmed Tight frame completions with prescribed norms
title_sort Tight frame completions with prescribed norms
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Ruiz, Mariano Andres
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andres
author_role author
author2 Ruiz, Mariano Andres
author2_role author
dc.subject.none.fl_str_mv FRAME
TIGHT FRAME COMPLETIONS
MAJORIZATION
topic FRAME
TIGHT FRAME COMPLETIONS
MAJORIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let H be a finite dimensional (real or complex) Hilbert space and let {a_i} ∞_i=1. be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {f_i}p_i=1 in H we find necessary and sufficient conditions for the existence of r ∈ N U {∞} and a Bessel sequence G = {g_i}r_i=1  in H such that F U G is a tight frame for H and || g_i ||^2 = a_i for every i. Moreover, in this case we compute the minimum r in NU {∞} with this property. We also describe algorithms that perform completions of a given set of vectors to tight frames.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
description Let H be a finite dimensional (real or complex) Hilbert space and let {a_i} ∞_i=1. be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {f_i}p_i=1 in H we find necessary and sufficient conditions for the existence of r ∈ N U {∞} and a Bessel sequence G = {g_i}r_i=1  in H such that F U G is a tight frame for H and || g_i ||^2 = a_i for every i. Moreover, in this case we compute the minimum r in NU {∞} with this property. We also describe algorithms that perform completions of a given set of vectors to tight frames.
publishDate 2008
dc.date.none.fl_str_mv 2008-01
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/11336/110304
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Tight frame completions with prescribed norms; Sampling Publishing ; Sampling Theory in Signal and Image Processing; 7; 1; 1-2008; 1-13
1530-6429
CONICET Digital
CONICET
url http://hdl.handle.net/11336/110304
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Tight frame completions with prescribed norms; Sampling Publishing ; Sampling Theory in Signal and Image Processing; 7; 1; 1-2008; 1-13
1530-6429
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://stsip.org/
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
application/pdf
dc.publisher.none.fl_str_mv Sampling Publishing
publisher.none.fl_str_mv Sampling Publishing
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_ 1842981146890076160
score 12.48226

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