A Painlevé equation for the Hörmander-Bernhardsson constant

Friedrich Littmann

The Hörmander-Bernhardsson constant $\mathcal{C}$ is the sharp constant in $|f(0)|\le \mathcal{C}\Vert f{\Vert }_1$ for entire functions of exponential type $\le \pi$. We prove that $\mathscr…