Schrödinger operators on graphs: Symmetrization and Eulerian cycles

DOI10.1090/proc12784zbMath1355.34053OpenAlexW2014057317MaRDI QIDQ2790197

G. Karreskog, I. Trygg Kupersmidt, Pavel Kurasov

Publication date: 3 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc12784

zbMATH Keywords

spectral propertieslowest eigenvaluemetric graphsSchrödinder operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (14)

Quantum trees which maximize higher eigenvalues are unbalanced ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ Quantum graphs which optimize the spectral gap ⋮ Optimal potentials for quantum graphs ⋮ Surgery transformations and spectral estimates of \(\delta\) beam operators ⋮ Eigenvalue estimates for the Laplacian on a metric tree ⋮ Edge connectivity and the spectral gap of combinatorial and quantum graphs ⋮ Spectral Monotonicity for Schrödinger Operators on Metric Graphs ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ On the hot spots of quantum graphs ⋮ The Krein-von Neumann extension for Schrödinger operators on metric graphs ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ Eigenvalue estimates for the Laplacian with anti-Kirchhoff conditions on a metric tree ⋮ Surgery principles for the spectral analysis of quantum graphs

Cites Work

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• Schrödinger operators on graphs and geometry I: Essentially bounded potentials
• Spectral gap for quantum graphs and their edge connectivity
• Quantum graphs: I. Some basic structures
• Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs
• Quantum Graphs and Their Applications
• Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

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