Slanted matrices, Banach frames, and sampling

Aldroubi, A.; Baskakov, A.; Krishtal, I.

Slanted matrices, Banach frames, and sampling

Authors

Aldroubi, A.

Baskakov, A.

Krishtal, I.

Description

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.