# Balian-Low type theorems on $L^2(\mathbb{C})$

## TL;DR

This paper establishes Balian-Low type theorems for the space of square-integrable functions on the complex plane, utilizing the Weyl transform and special Hermite operator, advancing the theoretical understanding of Gabor analysis.

## Contribution

It introduces new Balian-Low theorems on $L^2(C)$ specifically for the special Hermite operator, expanding the scope of time-frequency analysis.

## Key findings

- Proves amalgam Balian-Low theorems on $L^2(C)$
- Establishes Balian-Low type theorems using the Weyl transform
- Extends classical results to complex plane setting

## Abstract

In this paper we prove amalgam Balian-Low theorems and Balian-Low type theorems on $L^2(\mathbb{C})$ for the special Hermite operator using the Weyl transform.