# An invitation to Gabor analysis

## TL;DR

This paper introduces Gabor analysis, exploring its theoretical foundations, applications, and three open problems, highlighting its interdisciplinary significance across mathematics, engineering, and science.

## Contribution

It provides an accessible overview of Gabor analysis and discusses three open problems, contributing to the understanding and development of this field.

## Key findings

- Identification of three open problems in Gabor analysis
- Connection of Gabor analysis to wavelets and other fields
- Emphasis on the interdisciplinary nature of Gabor analysis

## Abstract

Gabor analysis which can be traced back to Dennis Gabor's influential 1946 paper \emph{Theory of communication}, is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of a given window function. It re-emerged with the advent of wavelets at the end of the last century and is now at the intersection of many fields of mathematics, applied mathematics, engineering, and science. The goal of this paper is to give a brief introduction to Gabor analysis by elaborating on three open problems.