Title
Frames and their associated H-F(p)-subspaces
Abbreviated Journal Title
Adv. Comput. Math.
Keywords
Frames; Riesz bases; Reconstruction; Dilation; LOCALIZATION; OPERATOR; OVERCOMPLETENESS; DENSITY; SYSTEMS; SPACES; Mathematics, Applied
Abstract
Given a frame F = {f(j)} for a separable Hilbert space H, we introduce the linear subspace H-F(p) of H consisting of elements whose frame coefficient sequences belong to the l(p)-space, where 1 < = p < 2. Our focus is on the general theory of these spaces, and we investigate different aspects of these spaces in relation to reconstructions, p-frames, realizations and dilations. In particular we show that for closed linear subspaces of H, only finite dimensional ones can be realized as H-F(p)-spaces for some frame F. We also prove that with a mild decay condition on the frame F the frame expansion of any element in H-F(p) converges in both the Hilbert space norm and the parallel to . parallel to(F, p-) norm which is induced by the l(p)-norm.
Journal Title
Advances in Computational Mathematics
Volume
34
Issue/Number
2
Publication Date
1-1-2011
Document Type
Article
Language
English
First Page
185
Last Page
200
WOS Identifier
ISSN
1019-7168
Recommended Citation
"Frames and their associated H-F(p)-subspaces" (2011). Faculty Bibliography 2010s. 1354.
https://stars.library.ucf.edu/facultybib2010/1354
Comments
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