Remark: Tangential annihilators are retained

The equations in (eq:completekernel) are distributional equations. They cannot be replaced by equations saying that the smooth scalar coefficients vanish pointwise. A nonzero distribution $T$ can be annihilated by a nonzero smooth function. For example, $x\delta (x)=0$. The criterion therefore retains, rather than suppresses, tangential annihilator relations.