# The Gabor wave front set of compactly supported distributions

## TL;DR

This paper establishes a precise relationship between the Gabor wave front set of compactly supported distributions and the classical wave front set, revealing that the former can be characterized via the projection of the latter.

## Contribution

It provides a new characterization of the Gabor wave front set for compactly supported distributions using classical wave front set projections.

## Key findings

- Gabor wave front set equals zero times the projection of the classical wave front set.
- Establishes a direct link between Gabor and classical wave front sets for compactly supported distributions.
- Offers a new perspective on analyzing distributions via time-frequency methods.

## Abstract

We show that the Gabor wave front set of a compactly supported distribution equals zero times the projection on the second variable of the classical wave front set.