Frame completions with prescribed norms: local minimizers and applications

Autores
Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let F0 = {fi}i∈In0 be a finite sequence of vectors in Cd and let a = (ai)i∈Ik be a finite sequence of positive numbers, where In = {1,...,n} for n ∈ N. We consider the completions of F0 of the form F = (F0, G) obtained by appending a sequence G = {gi}i∈Ik of vectors in Cd such that gi2 = ai for i ∈ Ik, and endow the set of completions with the metric d(F, F˜) = max{ gi − ˜gi : i ∈ Ik} where F˜ = (F0, G˜). In this context we show that local minimizers on the set of completions of a convex potential Pϕ, induced by a strictly convex function ϕ, are also global minimizers. In case that ϕ(x) = x2 then Pϕ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Rios, Noelia Belén. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Materia
Frame completions
Convex potential
Local minimum
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:11336/20215
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Frame completions with prescribed norms: local minimizers and applicationsMassey, Pedro GustavoRios, Noelia BelénStojanoff, DemetrioFrame completionsConvex potentialLocal minimumMajorizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let F0 = {fi}i∈In0 be a finite sequence of vectors in Cd and let a = (ai)i∈Ik be a finite sequence of positive numbers, where In = {1,...,n} for n ∈ N. We consider the completions of F0 of the form F = (F0, G) obtained by appending a sequence G = {gi}i∈Ik of vectors in Cd such that gi2 = ai for i ∈ Ik, and endow the set of completions with the metric d(F, F˜) = max{ gi − ˜gi : i ∈ Ik} where F˜ = (F0, G˜). In this context we show that local minimizers on the set of completions of a convex potential Pϕ, induced by a strictly convex function ϕ, are also global minimizers. In case that ϕ(x) = x2 then Pϕ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Rios, Noelia Belén. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaSpringer2017-04-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/20215Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Frame completions with prescribed norms: local minimizers and applications; Springer; Advances In Computational Mathematics; 12-4-2017; 1-361019-7168CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s10444-017-9535-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-017-9535-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:25:19Zoai:ri.conicet.gov.ar:11336/20215instacron: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 13:25:19.841CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Frame completions with prescribed norms: local minimizers and applications
title Frame completions with prescribed norms: local minimizers and applications
spellingShingle Frame completions with prescribed norms: local minimizers and applications
Massey, Pedro Gustavo
Frame completions
Convex potential
Local minimum
Majorization
title_short Frame completions with prescribed norms: local minimizers and applications
title_full Frame completions with prescribed norms: local minimizers and applications
title_fullStr Frame completions with prescribed norms: local minimizers and applications
title_full_unstemmed Frame completions with prescribed norms: local minimizers and applications
title_sort Frame completions with prescribed norms: local minimizers and applications
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_role author
author2 Rios, Noelia Belén
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv Frame completions
Convex potential
Local minimum
Majorization
topic Frame completions
Convex potential
Local minimum
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 F0 = {fi}i∈In0 be a finite sequence of vectors in Cd and let a = (ai)i∈Ik be a finite sequence of positive numbers, where In = {1,...,n} for n ∈ N. We consider the completions of F0 of the form F = (F0, G) obtained by appending a sequence G = {gi}i∈Ik of vectors in Cd such that gi2 = ai for i ∈ Ik, and endow the set of completions with the metric d(F, F˜) = max{ gi − ˜gi : i ∈ Ik} where F˜ = (F0, G˜). In this context we show that local minimizers on the set of completions of a convex potential Pϕ, induced by a strictly convex function ϕ, are also global minimizers. In case that ϕ(x) = x2 then Pϕ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Rios, Noelia Belén. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
description Let F0 = {fi}i∈In0 be a finite sequence of vectors in Cd and let a = (ai)i∈Ik be a finite sequence of positive numbers, where In = {1,...,n} for n ∈ N. We consider the completions of F0 of the form F = (F0, G) obtained by appending a sequence G = {gi}i∈Ik of vectors in Cd such that gi2 = ai for i ∈ Ik, and endow the set of completions with the metric d(F, F˜) = max{ gi − ˜gi : i ∈ Ik} where F˜ = (F0, G˜). In this context we show that local minimizers on the set of completions of a convex potential Pϕ, induced by a strictly convex function ϕ, are also global minimizers. In case that ϕ(x) = x2 then Pϕ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.
publishDate 2017
dc.date.none.fl_str_mv 2017-04-12
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/11336/20215
Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Frame completions with prescribed norms: local minimizers and applications; Springer; Advances In Computational Mathematics; 12-4-2017; 1-36
1019-7168
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20215
identifier_str_mv Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Frame completions with prescribed norms: local minimizers and applications; Springer; Advances In Computational Mathematics; 12-4-2017; 1-36
1019-7168
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://link.springer.com/10.1007/s10444-017-9535-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-017-9535-y
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
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 12.493442

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