Liouville Operators over the Hardy Space

TL;DR

This paper explores Liouville operators within the Hardy space framework, connecting complex differential equations to operator theory, which could enhance analysis techniques in control systems.

Contribution

It introduces the study of Liouville operators over the Hardy space, a novel approach linking complex ODEs with reproducing kernel Hilbert spaces.

Findings

Liouville operators encode complex ODEs in Hardy space.

New operator-theoretic methods for control system analysis.

Potential for improved dynamical systems understanding.

Abstract

The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade. This manuscript investigates Liouville operators over the Hardy space, which encode complex ordinary differential equations in an operator over a reproducing kernel Hilbert space.