Uniqueness of Gabor series

TL;DR

This paper proves that complete and minimal Gabor systems composed of Gaussian functions form a Markushevich basis in L^2(R), establishing a fundamental property of such systems in functional analysis.

Contribution

It demonstrates that Gaussian Gabor systems with completeness and minimality are Markushevich bases, a novel result linking Gabor analysis and basis theory.

Findings

Gabor systems of Gaussians are Markushevich bases under certain conditions.

The result bridges Gabor analysis with basis theory in L^2 spaces.

Provides a new perspective on the structure of Gabor systems.

Abstract

We prove that any complete and minimal Gabor system of Gaussians is a Markushevich basis in $L^2(\mathbb{R})$.