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Mollifier
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, mollifiers (also known as <i>approximations to the identity</i>) are particular <a href="/facts/Smooth_function/mffL4ch2">smooth functions</a>, used for example in <a href="/facts/Distribution_(mathematics)/yfaJ4mUp">distribution theory</a> to create <a href="/facts/Sequence/gV2S4uqp">sequences</a> of smooth functions approximating nonsmooth <a href="/facts/Generalized_function/fCM4VsyT">(generalized) functions</a>, via <a href="/facts/Convolution/PVPrdz9J">convolution</a>. 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. </p><p>They are also known as Friedrichs mollifiers after <a href="/facts/Kurt_Otto_Friedrichs/qHH9E0S4">Kurt Otto Friedrichs</a>, who introduced them. </p>