Convolution theorem for Laplace transforms ($\mathcal{L}(f\ast g)=\mathcal{L}f\mathcal{L}g$)

For functions whose Laplace transforms converge on a common right half-plane, the causal convolution $(f\ast g)(t)={\int }_0^{t}f(s)g(t-s)ds$ satisfies $\mathcal{L}(f\ast g)=\mathcal{L}(f)\mathcal{L}(g)$. This converts a transformed boundary forcing into a known time-domain integral representation.