IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Optimal dual frames and frame completions for majorization
Autor/es:
P. MASSEY; M. RUIZ; D. STOJANOFF
Revista:
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Año: 2013 vol. 34 p. 201 - 201
ISSN:
1063-5203
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.