2 problems

Let $\mathcal C$ be a proper closed convex subset of $\mathbb R^2$ with positive Lebesgue measure. Assume that $\operatorname{Op}^w(\mathbf 1_{\mathcal C})$ is a bounded self-adjoi…

Let $n\ge1$, $\alpha=(\alpha_1,\dots,\alpha_n)\in\mathbb N^n$, and $a=(a_1,\dots,a_n)\in(0,+\infty)^n$ be as in the Laguerre-integral conjecture, and let $K_\alpha(a)$ denote the c…