Slanted matrices, Banach frames, and sampling

Abstract

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.

Cited by in corpus (1)

• On the invertibility of "rectangular" bi-infinite matrices and applications in time--frequency analysis