Mollifier

A mollifier, also called an approximation to the identity or a Friedrichs mollifier after the mathematician Kurt Otto Friedrichs, is a smooth function used in distribution theory to build a sequence of smooth functions that approximate a function or generalized function that is not itself smooth. Convolving a rough function with a mollifier smooths, or mollifies, its sharp features while keeping the result close to the original function. Mollifiers are a basic tool of modern analysis because they let mathematicians prove that a property known to hold for smooth functions also holds more generally, by first smoothing out a nonsmooth function's discontinuities and rough spots and then taking a limit.