Harmonic Analysis on Metrized Graphs

By Matthew Baker, Robert Rumely. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2004

87 citations recorded by the source corpus.

Abstract This paper studies the Laplacian operator on a metrized graph, and its spectral theory.

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Zhang’s Conjecture and the Effective Bogomolov Conjecture over function fields (2009, methodology): “The functions jz(x, y) and r(x, y) are also studied in [ BR ], [BF], [C1], [C2], [C3],[C4], and [C5].”
A Hilbert Space Approach to Effective Resistance Metric (2009, background): “8) have also appeared in [3,35,36] and [29, Def.”
Metric properties of the tropical Abel–Jacobi map (2009, background): “Another shows that the canonical measure µZh on a metric graph Γ, defined by S. Zhang, measures lengths on Φp(Γ) with respect to the “sup-norm” on J(Γ).”
Potential Theory and Dynamics on the Berkovich Projective Line (2010, methodology): “In this chapter, we recall some basic facts about metrized graphs from [8].”