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arXiv · 2407.00970

The H\"ormander--Bernhardsson extremal function: A preliminary study

Andriy Bondarenko·Joaquim Ortega-Cerdà·Danylo Radchenko·Kristian Seip
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Abstract

We study the function $\varphi_1$ of minimal $L^1$ norm among all functions $f$ of exponential type at most $\pi$ for which $f(0)=1$. This function, first studied by H\"{o}rmander and Bernhardsson in 1993, has only real zeros $\pm \tau_n$, $n=1,2, \ldots$, and the sequence $(\tau_n-n-\frac12)$ has $\ell^2$ norm bounded by $0.13$. The zeros $\tau_n$ can be computed by means of a fixed point iteration.

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Andriy Bondarenko, Joaquim Ortega-Cerdà, Danylo Radchenko, Kristian Seip. 2024-07-01. The H\"ormander--Bernhardsson extremal function: A preliminary study. https://doi.org/10.1007/978-3-031-95551-8_4

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