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Mollifier

A mollifier (top) in dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version.

In mathematics, mollifiers (also known as approximations to the identity) are particular smooth functions, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. Intuitively, given a (generalized) function, convolving it with a mollifier "mollifies" it, that is, its sharp features are smoothed, while still remaining close to the original.[1]

They are also known as Friedrichs mollifiers after Kurt Otto Friedrichs, who introduced them.[2]

  1. ^ That is, the mollified function is close to the original with respect to the topology of the given space of generalized functions.
  2. ^ See (Friedrichs 1944, pp. 136–139).
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