Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10444-010-9149-0
Title: Frames and their associated Hp F-subspaces
Authors: Han, D.
Li, P.
Tang, W.-S. 
Keywords: Dilation
Frames
Reconstruction
Riesz bases
Issue Date: 2011
Citation: Han, D., Li, P., Tang, W.-S. (2011). Frames and their associated Hp F-subspaces. Advances in Computational Mathematics 34 (2) : 185-200. ScholarBank@NUS Repository. https://doi.org/10.1007/s10444-010-9149-0
Abstract: Given a frame F = {fj} for a separable Hilbert space H, we introduce the linear subspace Hp F of H consisting of elements whose frame coefficient sequences belong to the ℓp-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 Hp F-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 Hp F converges in both the Hilbert space norm and the {double pipe} ·{double pipe}F, p-norm which is induced by the ℓp-norm. © 2010 Springer Science+Business Media, LLC.
Source Title: Advances in Computational Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103299
ISSN: 10197168
DOI: 10.1007/s10444-010-9149-0
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