5 problems

Let $N$ be the number of points and let $(P_m)$ denote the property that the maximizer represented by regular polygons has the specified geometric extremal behavior for $m$ points.…

Let $\beta$ be the expansion parameter, let $a$ be the regularization parameter, and let $\psi_{a,\beta}(x)$ denote the function given by Theorem. At fixed $a$ and $x$, consider an…

Ground-state optimization conjecture. The inequality

Weighted Lorentz dispersive estimates conjecture. For every $\alpha\ne0$ and $y\in\mathbb{R}^3$, one has

Let $H_{\alpha,y}$ be the Schrödinger operator with a point interaction of strength $\alpha$ at $y\in\mathbb{R}^3$, let $P_{ac}$ denote the projection onto its absolutely continuou…