Smooth functions | Functional analysis

Mollifier

In mathematics, mollifiers (also known as approximations to the identity) are smooth functions with special properties, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. Intuitively, given a function which is rather irregular, by convolving it with a mollifier the function gets "mollified", that is, its sharp features are smoothed, while still remaining close to the original nonsmooth (generalized) function. They are also known as Friedrichs mollifiers after Kurt Otto Friedrichs, who introduced them. (Wikipedia).

Mollifier
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Mollifier | Support (mathematics) | Weak formulation | Generalized function | Integral operator | Derivative | Indicator function | Tosio Kato | Weierstrass transform | Distance | Differentiable function | Minkowski addition | Non-analytic smooth function | Banach space | Fritz John | Sequence | Variable (mathematics) | Elliptic partial differential equation | Multiplication | Mathematics | Kurt Otto Friedrichs | Dirac delta function | Function (mathematics) | Set (mathematics) | Distribution (mathematics) | Real number | Convolution | Hilbert space | Approximate identity | Bump function | Unit ball