Multiplication of a distribution by a smooth function
= Multiplication of a distribution by a smooth function
For a <distribution> $u$ and a <smooth function> $a$, the product $au$ is defined by $\langle au,\varphi\rangle=\langle u,a\varphi\rangle$. It obeys the <Leibniz rule>; in one dimension, $(au)'=a'u+au'$.