Frame completions with prescribed norms: local minimizers and applications

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 ∈...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Rios, Noelia Belén, Stojanoff, Demetrio
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2017
Materias:
Matemática
Frame completions
Convex potential
Local minimum
Majorization
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/100111
https://ri.conicet.gov.ar/11336/20215
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-100111
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Frame completions
Convex potential
Local minimum
Majorization
spellingShingle Matemática
Frame completions
Convex potential
Local minimum
Majorization
Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
Frame completions with prescribed norms: local minimizers and applications
topic_facet Matemática
Frame completions
Convex potential
Local minimum
Majorization
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.
format Articulo
Preprint
author Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_facet Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_sort Massey, Pedro Gustavo
title Frame completions with prescribed norms: local minimizers and applications
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
publishDate 2017
url http://sedici.unlp.edu.ar/handle/10915/100111
https://ri.conicet.gov.ar/11336/20215
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AT stojanoffdemetrio framecompletionswithprescribednormslocalminimizersandapplications
bdutipo_str Repositorios
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