Mollifier
Sign in to saveAlso known as mollifiers
thumb|A mollifier (top) in Dimension (mathematics)|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.
~9 min read
Article
16 sectionsContents
- Historical notes
- Definition
- Modern (distribution based) definition
- Notes on Friedrichs' definition
- Concrete example
- Properties
- Smoothing property
- Approximation of identity
- Support of convolution
- Applications
- Product of distributions
- "Weak=Strong" theorems
- Smooth cutoff functions
- See also
- Notes
- References
thumb|A mollifier (top) in Dimension (mathematics)|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.