What is a 'MOllifier' (function)

[tpm]

What is a Mollifier, and what are they used for??.. please don't refer to Wikipedia since i understand only a bit from article..

 

[matt grime]

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.

 

[tacman]

A mollifier function, also known as a smoothing function, is a mathematical function that is used to approximate a given function by making it smoother. It is typically used in the field of mathematical analysis to smooth out functions that are not smooth enough to be easily manipulated or analyzed.

The idea behind a mollifier is to create a function that is infinitely differentiable and has compact support, meaning that it is zero outside of a finite interval. This allows the mollifier to "smooth out" any sharp edges or discontinuities in a given function, making it easier to work with.

Mollifiers are often used in the study of partial differential equations, where they can be used to construct solutions to equations that may not have a smooth solution otherwise. They are also commonly used in the field of signal processing to remove noise from signals and make them easier to analyze.

In summary, a mollifier function is a tool used in mathematics to approximate and smooth out functions, making them easier to work with and analyze. It is a powerful tool that has many applications in various fields of mathematics and science.