The spherical phylon group and invariants of the Laplace transform

TL;DR

This paper introduces the spherical phylon group, a subgroup of formal diffeomorphisms fixing the origin, and uses its invariant theory to analyze invariants of the Laplace transform, advancing understanding in this mathematical area.

Contribution

It defines the spherical phylon group and applies its invariant theory to study Laplace transform invariants, a novel approach in this context.

Findings

Characterization of invariants of the Laplace transform

Introduction of the spherical phylon group as a new mathematical object

Application of invariant theory to Laplace transform analysis

Abstract

We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of $\R^d$ that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.