# The G-wavefront set and the twisted convolution product

## TL;DR

This paper establishes a criterion for when the twisted convolution product of two tempered distributions exists as a tempered distribution, providing examples of related algebraic structures within the space of tempered distributions.

## Contribution

It introduces a sufficient condition for the twisted convolution product to be well-defined as a tempered distribution and explores algebraic structures within this framework.

## Key findings

- Provided a criterion for the existence of the twisted convolution product.
- Listed examples of algebras under the twisted convolution and related products.
- Connected the results to the G-wavefront set and the structure of tempered distributions.

## Abstract

We give a sufficient criterion for the existence of the twisted convolution product of two tempered distributions as a tempered distribution, and we list examples of algebras with respect to this and related products contained in $\mathscr S^\prime$.