The Hörmander--Bernhardsson extremal function: A preliminary study

Paper

Abstract

We study the function

of minimal

norm among all functions

of exponential type at most

for which

. This function, first studied by Hörmander and Bernhardsson in 1993, has only real zeros

, and the sequence

has

norm bounded by

. The zeros

can be computed by means of a fixed point iteration.