Remarks on multivariate Gaussian Gabor frames

TL;DR

This paper explores the complex behavior of multivariate Gaussian Gabor frames in higher dimensions, highlighting differences from the well-understood one-dimensional case and emphasizing the need for further research.

Contribution

It provides initial insights into multivariate Gaussian Gabor systems, revealing their intricate nature beyond the known lattice density characterization in one dimension.

Findings

Higher-dimensional Gaussian Gabor systems exhibit complex behavior.

Existing one-dimensional characterizations do not directly extend to higher dimensions.

Further exploration is necessary to understand these systems fully.

Abstract

We report on initial findings on Gabor systems with multivariate Gaussian window. Unlike the existing characterisation for dimension one in terms of lattice density, our results indicate that the behavior of Gaussians in higher-dimensional Gabor systems is intricate and further exploration is a valuable and challenging task.