Criticality theory for Schr\"odinger operators on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
TL;DR
This paper develops a criticality theory for Schrödinger operators on infinite weighted graphs, extending the understanding of their spectral properties and behavior in a graph-theoretic context.
Contribution
It introduces a novel criticality framework for Schrödinger operators on general weighted graphs, broadening the scope of spectral analysis in graph theory.
Findings
Established a classification of Schrödinger operators into critical and subcritical cases.
Provided new criteria for the criticality of operators on infinite graphs.
Extended classical results from Euclidean spaces to graph settings.
Abstract
We study Schr\"odinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schr\"odinger operators on general weighted graphs.
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