Convolution

Convolution of $f(t)$ and $g(t)$ denoted $(f\ast g)(t)$ is

Properties

Commutativity

$f\ast g=g\ast f$

Distributivity

$f\ast (g+h)=(f\ast g)+(f\ast h)$

Associativity

$(f\ast g)\ast h=f\ast (g\ast h)$

Zero

$f\ast 0=0$

Theorem

If $f(t)$ and $g(t)$ are piecewise continuous and of exponential order for $t\ge 0$, then so is $(f\ast g)(t)$ and