Convolution quotient

In mathematics, a convolution quotient is to the operation of convolution as a quotient of integers is to multiplication. Convolution quotients were introduced by Mikusiński (1949), and their theory is sometimes called Mikusiński's operational calculus. For two functions ƒ, g, the pair (ƒ, g) has the same convolution quotient as the pair (h * ƒ,h * g).

Convolution quotients are used in an approach to making Dirac's delta function and other generalized functions logically rigorous.

References

• Mikusiński, Jan G. (1949), "Sur les fondements du calcul opératoire", Studia Math., 11: 41–70, MR 0036949
• Mikusiński, Jan (1959) [1953], Operational calculus, International Series of Monographs on Pure and Applied Mathematics, 8, New York-London-Paris-Los Angeles: Pergamon Press, MR 0105594