# The essential spectrum of canonical systems

## TL;DR

This paper investigates the essential spectrum of canonical systems using oscillation theory, providing a more quantitative characterization of systems with purely discrete spectra compared to previous work.

## Contribution

It offers a generalized, quantitative analysis of the essential spectrum of canonical systems, extending recent characterizations of purely discrete spectra.

## Key findings

- Characterization of the essential spectrum for canonical systems
- Quantitative criteria for purely discrete spectrum
- Extension of previous spectral analysis results

## Abstract

We study the minimum of the essential spectrum of canonical systems $Ju'=-zHu$. Our results can be described as a generalized and more quantitative version of the characterization of systems with purely discrete spectrum, which was recently obtained by Romanov and Woracek [6]. Our key tool is oscillation theory.