Schrödinger operators on graphs and geometry I: Essentially bounded potentials

DOI10.1016/j.jfa.2007.11.007zbMath1140.81387OpenAlexW2115361119MaRDI QIDQ2472867

Pavel Kurasov

Publication date: 25 February 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2007.11.007

zbMATH Keywords

Euler characteristicquantum graphTrace formula

Mathematics Subject Classification ID

Applications of graph theory (05C90) General topics in linear spectral theory for PDEs (35P05) Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Characteristic classes and numbers in differential topology (57R20) Isospectrality (58J53)

Related Items (18)

Concrete method for recovering the Euler characteristic of quantum graphs ⋮ Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples ⋮ Inverse Sturm-Liouville problem for a star graph by three spectra ⋮ Optimal potentials for quantum graphs ⋮ Rayleigh estimates for differential operators on graphs ⋮ Spectral determinants and an Ambarzumian type theorem on graphs ⋮ Quantum graphs: PT-symmetry and reflection symmetry of the spectrum ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ Gluing graphs and the spectral gap: a Titchmarsh–Weyl matrix-valued function approach ⋮ Stable polynomials and crystalline measures ⋮ Compressed resolvents and reduction of spectral problems on star graphs ⋮ Inverse problems for Aharonov–Bohm rings ⋮ ON SEMICLASSICAL AND UNIVERSAL INEQUALITIES FOR EIGENVALUES OF QUANTUM GRAPHS ⋮ Diffusion processes in thin tubes and their limits on graphs ⋮ Schrödinger operators on graphs: Symmetrization and Eulerian cycles ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem ⋮ Asymptotics and estimates for spectral minimal partitions of metric graphs ⋮ Laplacians on bipartite metric graphs

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