On the stability under convolution of resurgent functions

TL;DR

This paper proves that the space of resurgent functions remains stable under convolution when the set of singularities is closed, discrete, and stable under addition, providing a self-contained mathematical proof.

Contribution

It offers a self-contained proof of the convolution stability of resurgent functions with singularities stable under addition.

Findings

Resurgent functions are stable under convolution.

Stability holds when the singularity set is closed, discrete, and additive.

The proof is self-contained and rigorous.

Abstract

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that this set be stable under addition.