# Hermite expansions of some tempered distributions

## TL;DR

This paper develops a method to compute Hermite expansions of tempered distributions using the Bargmann transform, offering advantages over direct methods especially in complex and higher-dimensional cases.

## Contribution

It introduces a novel approach leveraging the Bargmann transform to efficiently compute Hermite expansions of tempered distributions.

## Key findings

- Method simplifies Hermite expansion calculations.
- Effective in higher-dimensional cases.
- Improves upon direct computation methods.

## Abstract

We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the direct computations in the shifts of singularities and the higher dimensional cases.