A quantitative Balian-Low theorem for higher dimensions

TL;DR

This paper generalizes the quantitative Balian-Low theorem to higher-dimensional spaces, providing a broader understanding of the theorem's implications in multiple dimensions.

Contribution

It introduces a higher-dimensional extension of the quantitative Balian-Low theorem, expanding its applicability beyond the original setting.

Findings

Extended the theorem to higher dimensions

Provided new bounds for Gabor systems in multiple dimensions

Enhanced understanding of time-frequency localization in higher-dimensional spaces

Abstract

We extend the quantitative Balian-Low theorem of Nitzan and Olsen to higher dimensions.