[Banach] Abstract of a paper by Morten Nielsen

This is an announcement for the paper "On Schauder Bases Properties of Multiply Generated Gabor Systems" by Morten Nielsen.

Abstract: Let $A$ be a finite subset of $L^2(\mathbb{R})$ and $p,q\in\mathbb{N}$. We characterize the Schauder basis properties in $L^2(\mathbb{R})$ of the Gabor system $$G(1,p/q,A)={e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z}, g\in A},$$ with a specific ordering on $\mathbb{Z}\times \mathbb{Z}\times A$. The characterization is given in terms of a Muckenhoupt matrix $A_2$ condition on an associated Zibulski-Zeevi type matrix.

Archive classification: math.FA

Mathematics Subject Classification: 42C15, 46B15, 42C40

Remarks: 14 pages

Submitted from: mnielsen@math.aau.dk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1501.05794

or

http://arXiv.org/abs/1501.05794