Friedrich Littmann

A Painlev\'e equation for the H\"ormander-Bernhardsson constant

The H\"ormander-Bernhardsson constant $\mathscr{C}$ is the sharp constant in $|f(0)|\le \mathscr{C} \|f\|_1$ for entire functions of exponential type $\le \pi$. We prove that $\mathscr{C} = 2\pi \theta_*^{-2}$ where $\theta_*$ is the least positive singularity of the regular solution $v$ with $v(0)=0$ of the cosh-Gordo...