B. Delarue

Distributional zero divisors with full support

We show that every smooth manifold $M$ of positive dimension admits fully supported distributions $u,v\in \mathcal D'(M)$ with $\mathrm{WF}(u)\cap({-}\mathrm{WF}(v))=\emptyset$ and $uv=0$. Neither factor can be continuous on any non-empty open set, but $u$ may be chosen of optimal Sobolev order $\dim M/2$, with wavefro...