Artículo
Optimal dual frames and frame completions for majorization
Fecha de publicación:
03/2013
Editorial:
Academic Press Inc Elsevier Science
Revista:
Applied And Computational Harmonic Analysis
ISSN:
1063-5203
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto?Fickusʼ frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
Palabras clave:
Dual Frames
,
Frame Completions
,
Majorization
,
Schur-Horn
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Stojanoff, Demetrio; Ruiz, M; Massey, Pedro Gustavo; Optimal dual frames and frame completions for majorization; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 34; 2; 3-2013; 201-223
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