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dc.contributor.author
Benac, Maria Jose
dc.contributor.author
Massey, Pedro Gustavo
dc.contributor.author
Ruiz, Mariano Andres
dc.contributor.author
Stojanoff, Demetrio
dc.date.available
2024-02-14T11:22:51Z
dc.date.issued
2023-01
dc.identifier.citation
Benac, Maria Jose; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal (α,d)-multi-completion of d-designs; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 62; 1-2023; 331-364
dc.identifier.issn
1063-5203
dc.identifier.uri
http://hdl.handle.net/11336/226724
dc.description.abstract
Given finite sequences d=(dj)j∈Im∈Nm and α=(αi)i∈In∈R>0n of dimensions and weights (where Ik={1,?,k}, for k∈N), we consider the set D(α,d) of (α,d)-designs, i.e. m-tuples Φ=(Fj)j∈Im such that each Fj={fi,j}i∈In∈(Cdj)n and ∑j∈Im‖fi,j‖2=αi for i∈In. In this work we solve the optimal (α,d)-completion problem of an initial d-design Φ0=(Fj0)j∈Im with Fj0∈(Cdj)k, for j∈Im. Explicitly, given an strictly convex function φ:[0,∞)→[0,∞), we compute the (α,d)-designs Φφop that are (local) minimizers of the joint convex potential Pφ(Φ0,Φ)=∑j∈Imtr(φ[S(Fj0,Fj)]) of the multi-completions (Φ0,Φ), among all (α,d)-designs Φ=(Fj)j∈Im; here S(Fj0,Fj) denotes the frame operator of the completed sequence (Fj0,Fj)∈(Cdj)k+n, for j∈Im. We obtain the geometrical and spectral features of these optimal (α,d)-multi-completions. We further show that the optimal (α,d)-designs Φφop as above do not depend on φ. We also consider some reformulations and applications of our main results in different contexts in frame theory. Finally, we describe a fast finite step algorithm for computing optimal multi-completions that becomes relevant for the applications of our results and present some numerical examples of optimal multi-completions with prescribed weights.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
CONVEX POTENTIALS
dc.subject
FRAME COMPLETIONS
dc.subject
FRAMES
dc.subject
MAJORIZATION
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Optimal (α,d)-multi-completion of d-designs
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-02-09T14:34:10Z
dc.journal.volume
62
dc.journal.pagination
331-364
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Benac, Maria Jose. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Stojanoff, Demetrio. 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. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
dc.journal.title
Applied And Computational Harmonic Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S1063520322000811
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.acha.2022.10.002
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