On the Laplace transform

TL;DR

This paper establishes sufficient conditions for a function to be recognized as the Laplace transform of a function or distribution, without prior assumptions on the original function's properties or support.

Contribution

It provides new criteria for identifying Laplace transforms without assuming initial conditions or support restrictions on the original function.

Findings

Derived conditions for Laplace transform characterization

No assumptions on the original function's support or initial values

Applicable to functions and distributions alike

Abstract

Sufficient conditions are given for a function $F(p)$ to be the Laplace transform of a function $f(t)$ or a distribution $f$. No assumption on $f$ is given a priori. It is not even assumed that $f=0$ for $t<0$.