Is $\partial \partial H=0$ where H is the Heaviside function? In other words, I know that $\partial H=\delta$ but do two partials make it $0$?
2026-04-08 06:07:26.1775628446
Is $\partial \partial H=0$ where H is the Heaviside function?
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No, the distributional derivative of $\delta$ is not zero: for any test function $\phi$ we have $$\langle H'', \phi \rangle = \langle \delta', \phi \rangle = -\langle \delta, \phi' \rangle = \phi'(0),$$ which is in general non-zero.