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
If you mollify someone, you do or say something to make them less upset or angry. The investigation was undertaken primarily to mollify pressure groups. = placate. to make someone feel less angry and upset about something = placate (mollifier, from mollificare, from mollis )