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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 |
Appears in Collections: | Staff Publications |
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