Arkiv för Matematik

Volume 61 (2023)

Number 2

Overcompleteness of coherent frames for unimodular amenable groups

Pages: 277 – 299

DOI: https://dx.doi.org/10.4310/ARKIV.2023.v61.n2.a2

Authors: Martijn Caspers; Jordy Timo van Velthoven

Abstract

This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positive Beurling density can be removed yet still leave a frame. The obtained results extend various theorems of $\href{http://www.ams.org/mathscinet-getitem?mr=2235170}{[\textrm{J. Fourier Anal. Appl., 12(3):307-344, 2006}]}$ to frames with non-Abelian index sets.

Keywords

Beurling density, coherent system, frame, overcompleteness

2010 Mathematics Subject Classification

42C30, 46B15

Full Text (PDF format)

M.C. is supported by the NWO Vidi grant ‘Non-commutative harmonic analysis and rigidity of operator algebras’, VI.Vidi.192.018.

J.v.V. gratefully acknowledges support from the Austrian Science Fund (FWF) project J-4555.

Received 8 September 2022

Received revised 13 February 2023

Accepted 24 February 2023

Published 13 November 2023