Slanted matrices, Banach frames, and sampling

Details Slanted matrices, Banach frames, and sampling Slanted matrices, Banach frames, and sampling

2007-05-29

arxiv.org/abs/0705.4304v1

Mathematics

Functional Analysis

Scientific paper

In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted matrices boundedness below of the corresponding operator in $\ell^p$ for some $p$ implies boundedness below in $\ell^p$ for all $p$. We use the established resultto enrich our understanding of Banach frames and obtain new results for irregular sampling problems. We also present a version of a non-commutative Wiener's lemma for slanted matrices.

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