The Mikusinski operational calculus

The Mikusinski Operational Calculus is derived from a commutative ring of continuous functions a, b, ... in which the addition and multiplication (convolution) operations are a + b = {a(t) + b(t)} ab = {[integral 0 to t]a(t-[tau]b([tau])d[tau]}. By the Theorem of Titchmarsh, this ring has no divisors of zero-if ab = 0, then a = 0 or b = 0. Thus the ring may be extended to a field of convolution quotients a/b, b / 0. Here a/b is of an equivalence class such that [...]