Laplace transforms and valuations

TL;DR

This paper characterizes the classical Laplace transform as a continuous valuation with specific covariance properties, establishing that these properties uniquely define the transform.

Contribution

It provides a characterization of the Laplace transform based on valuation and covariance properties, linking classical analysis with valuation theory.

Findings

Laplace transform is a continuous valuation.

It is positively GL(n) covariant.

It is logarithmic translation covariant.

Abstract

It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.