The Hardy space from an engineer's perspective

TL;DR

This paper provides an accessible overview of Hardy spaces tailored for engineers, connecting classical signal theory with modern mathematical concepts to facilitate interdisciplinary understanding.

Contribution

It offers a beginner-friendly dictionary linking Hardy spaces with signals and systems theory, bridging gaps between mathematics and engineering disciplines.

Findings

Clarifies the relationship between Hardy spaces and control theory

Provides foundational explanations suitable for beginners

Connects classical signal concepts with modern mathematical frameworks

Abstract

We give an overview of parts of the theory of Hardy spaces from the viewpoint of signals and systems theory. There are books on this topic, which dates back to Bode, Nyquist, and Wiener, and that eventually led to the developement of $H^{\infty}$ optimal control. Our modest goal here is giving a beginner's dictionary for mathematicians and engineers who know little of either systems or $H^2$ spaces.