A Simple Proof of Nehari's Theorem Based on Duality

TL;DR

This paper presents a straightforward proof of Nehari's theorem on optimal approximation by $H_ fty$ functions, utilizing convex duality principles to simplify the understanding of the theorem.

Contribution

It offers a new, simplified proof of Nehari's theorem leveraging convex duality, enhancing theoretical understanding.

Findings

Simplified proof of Nehari's theorem using convex duality

Clarification of the theorem's theoretical foundations

Potential for easier application in control theory

Abstract

In this technical note we provide a simple proof of Nehari's theorem on the optimal approximation by $H_\infty$ functions, based on convex duality.