On the decomposition of the Laplacian on metric graphs

DOI10.1007/s00023-019-00879-zzbMath1432.05061arXiv1901.00349OpenAlexW3101308024WikidataQ126419290 ScholiaQ126419290MaRDI QIDQ2291625

Netanel Levi, Jonathan Breuer

Publication date: 31 January 2020

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.00349

zbMATH Keywords

decompositiondiscrete Laplaciandirect sum of one-dimensional operatorsfamily preserving metric graphsSchrödinger operators on metric trees

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (8)

A note on the Gaffney Laplacian on infinite metric graphs ⋮ Erratum to Spectral analysis of certain spherically homogeneous graphs, Operators and Matrices, 7 (2013), 825-847 ⋮ Self‐adjoint and Markovian extensions of infinite quantum graphs ⋮ Quantum graphs on radially symmetric antitrees ⋮ Spectra of regular quantum trees: rogue eigenvalues and dependence on vertex condition ⋮ Localization for Anderson models on metric and discrete tree graphs ⋮ Zero measure and singular continuous spectra for quantum graphs ⋮ Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree

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