Some spectral comparison results on infinite quantum graphs

TL;DR

This paper investigates spectral comparison results for Schrödinger operators on infinite quantum graphs, revealing new features like a modified local Weyl law and setting the stage for further research in this area.

Contribution

It extends spectral comparison results from finite to infinite quantum graphs and uncovers new spectral features unique to the infinite case.

Findings

Spectral comparison results established for infinite quantum graphs.

Identification of a modified local Weyl law on infinite graphs.

Foundation laid for future research on spectral properties of infinite metric graphs.

Abstract

In this paper we establish spectral comparison results for Schr\"odinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite quantum graphs such as a modified local Weyl law. In this sense, we regard this paper as a starting point for a more thorough investigation of spectral comparison results on more general infinite metric graphs.