On the Decomposition of the Laplacian on Metric Graphs

Jonathan Breuer, Netanel Levi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to the structure of the graph. Such decompositions have been extremely useful in the study of Schrödinger operators on metric trees. We show that the tree structure is not essential, and moreover, obtain a direct and simple correspondence between such decompositions in the discrete and continuum case.

Original languageAmerican English
Pages (from-to)499-537
Number of pages39
JournalAnnales Henri Poincare
Issue number2
StatePublished - 1 Feb 2020

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