dc.creatorMassey, Pedro Gustavo
dc.creatorRios, Noelia Belén
dc.creatorStojanoff, Demetrio
dc.date2017-04-12
dc.date2020-07-07T14:34:21Z
dc.date.accessioned2023-07-14T20:39:34Z
dc.date.available2023-07-14T20:39:34Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/100111
dc.identifierhttps://ri.conicet.gov.ar/11336/20215
dc.identifierissn:1019-7168
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7440099
dc.descriptionLet 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.
dc.descriptionFacultad de Ciencias Exactas
dc.formatapplication/pdf
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.subjectMatemática
dc.subjectFrame completions
dc.subjectConvex potential
dc.subjectLocal minimum
dc.subjectMajorization
dc.titleFrame completions with prescribed norms: local minimizers and applications
dc.typeArticulo
dc.typePreprint


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