# Fundamental solutions for a class of non-elliptic homogeneous differential operators

## TL;DR

This paper develops a method to explicitly compute fundamental solutions for a class of non-elliptic homogeneous differential operators with real-principal type symbols, using analytic continuation and invariant distributions.

## Contribution

It introduces a novel approach to construct fundamental solutions for non-elliptic operators via analytic continuation of meromorphic distributions.

## Key findings

- Explicit formulas for fundamental solutions derived
- Method applicable to a broad class of non-elliptic operators
- Connections established between fundamental solutions and invariant distributions

## Abstract

We compute temperate fundamental solutions of homogeneous differential operators with real-principal type symbols. Via analytic continuation of meromorphic distributions, fundamental solutions for these non-elliptic operators can be constructed in terms of radial averages and invariant distributions on the unit sphere.