On the Absolutely Continuous Spectrum of Sturm-Liouville Operators with Applications to Radial Quantum Trees

TL;DR

This paper develops criteria linking solution boundedness to the absence of subordinate solutions in Sturm-Liouville operators and applies these results to analyze the absolutely continuous spectrum of radial quantum trees.

Contribution

It introduces new criteria for the absence of subordinate solutions in Sturm-Liouville operators and applies them to quantum trees, extending spectral analysis methods.

Findings

Bounded solutions imply no subordinate solutions in Sturm-Liouville operators.

Established a Weidmann-type result for general Sturm-Liouville operators.

Analyzed the absolutely continuous spectrum of radially symmetric quantum trees.

Abstract

We consider standard subordinacy theory for general Sturm--Liouville operators and give criteria when boundedness of solutions implies that no subordinate solutions exist. As applications, we prove a Weidmann-type result for general Sturm--Liouville operators and investigate the absolutely continuous spectrum of radially symmetric quantum trees.