Harmonic analysis on metrized graphs
Matthew Baker, Robert Rumely
TL;DR
This paper investigates the properties of the Laplacian operator on metrized graphs, focusing on its eigenfunctions and spectral characteristics, to deepen understanding of harmonic analysis in this geometric setting.
Contribution
It introduces a framework for analyzing the Laplacian on metrized graphs and characterizes its eigenfunctions, advancing the mathematical theory of harmonic analysis on these structures.
Findings
Eigenfunctions of the Laplacian are characterized.
Spectral properties of the Laplacian on metrized graphs are analyzed.
New methods for harmonic analysis on graphs are proposed.
Abstract
We study the Laplacian on a metrized graph, and its eigenfunctions.
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Taxonomy
TopicsGraph theory and applications · Topological and Geometric Data Analysis · Matrix Theory and Algorithms