Seminar: The Hörmander--Bernhardsson function in higher dimensions

Antonio Pedro Ramos examines point-evaluation bounds for integrable functions of spherical exponential type in the multivariable Paley–Wiener space. Radial extremizers connect the problem to a weighted space in one variable. The talk establishes a third-order linear differential equation with polynomial coefficients in every dimension, extending the previously known odd-dimensional result. It also develops interpolation and reciprocal identities using the extremizer’s zeros. The research is joint work with Felipe Gonçalves and Danylo Radchenko.