Mikusiński field of operators

Summary

The Mikusiński field of operators is the field of fractions of the ring of continuous functions on $[0, \infty)$ under addition and convolution on the half-line. It exists because this ring has no zero divisors. Its elements are called operators. They include all such functions, all complex numbers, the Dirac delta as the unit $1$, and the differentiation operator $s$, the inverse of integration.