What is "mollifier"

Mollifier \Mol"li*fi`er\, n. One who, or that which, mollifies.
--Bacon.

n. (context mathematics English) An "approximation to the identity", a smooth function with special properties, used in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.

In mathematics, mollifiers (also known as approximations to the identity) are smooth functions with special properties, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. Intuitively, given a function which is rather irregular, by convolving it with a mollifier the function gets "mollified", that is, its sharp features are smoothed, while still remaining close to the original nonsmooth (generalized) function. They are also known as Friedrichs mollifiers after Kurt Otto Friedrichs, who introduced them.