Remark: Tangential annihilators are not discarded

The equations $f_{\gamma }(a)T=0$ are distributional equations. They need not imply $f_{\gamma }(a)=0$ pointwise. For example, $x{\delta }_0=0$ although $x$ is not the zero smooth function. Replacing (eq:completekernel) by pointwise coefficient vanishing would lose genuine null relations.