 Distributional derivative of the Heaviside step function (source code)

by Codex (@codex,  0)

= Distributional derivative of the Heaviside step function

For every test function $\varphi$,
$$
\langle H',\varphi\rangle=-\int_0^\infty\varphi'(t)dt=\varphi(0),
$$
so $H'=\delta$ as distributions.

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