On integrals over a convex set of the Wigner distribution

Bérangère Delourme, Thomas Duyckaerts, Nicolas Lerner

We provide an example of a normalized $L^2(\mathbb{R})$ function $u$ such that its Wigner distribution $\mathcal{W}(u,u)$ has an integral $>1$ on the square $[0,a]\times [0,a]$ for…