Mean-periodic function

In mathematical analysis, the concept of a mean-periodic function is a generalization introduced by Jean Delsarte, of the concept of a periodic function.

Consider a complex-valued function ƒ of a real variable. The function ƒ is periodic with period a precisely if for all real x, we have ƒ(x) − ƒ(x − a) = 0. This can be written as