What is a 'MOllifier' (function)

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A Mollifier is a mathematical function used to smooth other functions through convolution, resulting in smoother outputs. It is particularly effective when convolving with step functions, transforming them into continuous functions that are constant within compact sets and zero outside small neighborhoods. While the concept is straightforward, its practical applications may not be immediately apparent to everyone. The discussion encourages seeking clarification on specific aspects of the topic for better understanding. Overall, Mollifiers serve as useful tools in analysis for creating smoother functions from less regular ones.
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What is a Mollifier, and what are they used for??.. please don't refer to Wikipedia since i understand only a bit from article..
 
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Reading wikipedia it seems straightforward to me - it is a function that, when convolved with something, makes it smoother in an appropriate sense. The use it gives seems eminently easy to understand too - convolving step functions (indicator functions) one obtains 'nice' functions constant on given compact sets, and zero outside an arbitrarly small open set around the compact set. Personally, I don't see any use for it, but it isn't mathematically complicated.

Perhaps, since you find that wiki article incomprehensible, you might go through it and ask for elucidation on the precise parts that you don't get.
 

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