Title

Frames And Their Associated HPF-Subspaces

Keywords

Dilation; Frames; Reconstruction; Riesz bases

Abstract

Given a frame F = {fj} for a separable Hilbert space H, we introduce the linear subspace HpF 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 HpF-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 HpF 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.

Publication Date

2-1-2011

Publication Title

Advances in Computational Mathematics

Volume

34

Issue

2

Number of Pages

185-200

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10444-010-9149-0

Socpus ID

78651455572 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78651455572

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