Coherent frames with zero Beurling density

TL;DR

This paper demonstrates the existence of a coherent frame within the orbit of certain Lie groups, even when the index set's lower Beurling density is zero, expanding understanding of frame theory in mathematical analysis.

Contribution

It establishes the existence of coherent frames with zero Beurling density in the orbit of specific Lie groups, a novel result in frame theory.

Findings

Existence of coherent frames with zero Beurling density proven

Frames exist in the orbit of certain Lie groups with exponential growth

Advances understanding of frame density and structure in mathematical analysis

Abstract

We show the existence of a coherent frame in the orbit of a connected, simply connected unimodular solvable Lie group of exponential growth for which the lower Beurling density of its index set is zero.