4 problems

Let $a_{1,2}(t,\mathbf{x},\mathbf{k})$ denote the Wigner-distribution components associated with the two wave modes in the random hyperbolic system. Ensemble averaging means averag…

Let $f\in L^2(\mathbb{R})$, and let $g$ be a characteristic function of an interval. Interval-characteristic-function conjecture. The Wigner distribution $W(f,g)$ has zeros for eve…

Let $f$ and $g$ be finite linear combinations of Hermite functions, and call their Wigner distribution zero-free if it has no zeros. Nonexistence conjecture. No zero-free Wigner di…

Let $A$ denote the abelian subgroup governing the relevant geodesic or higher-rank flow, and let Wigner distributions be the associated semiclassical distributions; a limit of a Wi…