The Laplace Transform

A function f(t) is called original function if: 1. f(t) ≡ 0 for t < 0, 2. \(|f(t)| 0 with \(M > 0, s_0\in \mathbb {R}\). 3. For every closed interval [a, b], the function satisfies the Dirichlet conditions: (a) is bounded, (b) or is continuous, or has a finite number of discontinuities of first kind, (c) has a finite number of extremes.