2 problems

Let $\chi$ be a Schwartz function satisfying … and let $S_\tau$ be the Fourier multiplier with symbol $\chi((|\xi|-1)/\tau)$, where $0<\tau<1$. Thin-annuli formulation of the Bochn…

Sharpness conjecture. For each $\kappa\in[0,1/2]$, there exists a convex domain $\Omega$ with $\kappa_{\Omega}=\kappa$ such that