Overcompleteness of coherent frames for unimodular amenable groups

TL;DR

This paper investigates the overcompleteness of coherent frames in unimodular amenable groups, showing that certain dense subsets can be removed while maintaining the frame property, extending previous theorems to non-Abelian groups.

Contribution

It extends existing theorems on frame overcompleteness to the setting of non-Abelian unimodular amenable groups, highlighting the removal of dense subsets without losing the frame.

Findings

Positive Beurling density sets can be reduced while preserving frames

Extends prior results from Abelian to non-Abelian groups

Provides new insights into the structure of coherent frames in complex groups

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 [J. Fourier Anal. Appl., 12(3):307-344, 2006] to frames with non-Abelian index sets.