On the Decomposition of the Laplacian on Metric Graphs
arXiv:1901.00349 · doi:10.1007/s00023-019-00879-z
Abstract
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.
arXiv comment36 pages
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Cited by in corpus (5)
- Self-adjoint and Markovian extensions of infinite quantum graphs
- Zero Measure and Singular Continuous Spectra for Quantum Graphs
- A note on the Gaffney Laplacian on infinite metric graphs
- Embedded trace operator for infinite metric trees
- Spectra of Regular Quantum Trees: Rogue Eigenvalues and Dependence on Vertex Condition