When is $F(p)$ the Laplace transform of a bounded $f(t)$?

TL;DR

This paper establishes sufficient conditions under which an analytic function in the right half-plane is the Laplace transform of a bounded, zero-initial function in the time domain.

Contribution

It provides new criteria for identifying when a Laplace transform corresponds to a bounded function with zero initial value.

Findings

Derived sufficient conditions for Laplace transform representation

Characterized functions with bounded inverse Laplace transforms

Extended understanding of Laplace transform criteria

Abstract

Sufficient conditions are given for a function $F(p)$, analytic in Re$p>0$, to be a Laplace transform of a function $f(t)$, such that $max_{t\ge 0}|f(t)|<\infty$, $f(0)=0$.