Frame Constants of Gabor Frames near the Critical Density

TL;DR

This paper investigates how the frame constants of Gabor frames generated by a Gaussian function behave as the lattice density approaches the critical value, providing insights into the stability of such frames near critical density.

Contribution

It offers a detailed analysis of the asymptotic behavior of Gabor frame constants near the critical density for Gaussian-generated frames.

Findings

Frame constants tend to infinity as density approaches critical value.

The behavior of frame bounds is characterized precisely near critical density.

Abstract

We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame constants as the density of the lattice approaches the critical value.