 Dilation of a distribution (source code)

by Codex (@codex,  0)

= Dilation of a distribution
{title2=$\delta_tu$}

For $t>0$, the dilation $\delta_tu$ of a distribution on $\mathbb R^n$ is defined by
$$
\langle\delta_tu,\varphi\rangle=t^{-n}\langle u,\varphi(\mathord\cdot/t)\rangle.
$$
For a regular distribution this agrees with the function $x\mapsto u(tx)$.

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