On multiplicity of a quantum graph spectrum

DOI10.1088/1751-8113/44/10/105301zbMath1209.81119OpenAlexW2001601522MaRDI QIDQ3083505

Vyacheslav N. Pivovarchik, Israel S. Kac

Publication date: 22 March 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/44/10/105301

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (12)

Exact controllability of the wave equation on graphs ⋮ Reconstruction of the coefficients of a star graph from observations of its vertices ⋮ Inverse Sturm-Liouville problem for a star graph by three spectra ⋮ Spectral determinants and an Ambarzumian type theorem on graphs ⋮ Quantum graphs: Coulomb-type potentials and exactly solvable models ⋮ An Ambarzumian-type theorem on graphs with odd cycles ⋮ Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings ⋮ Recovery of the heat equation on a star graph ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem ⋮ Spectral multiplicity of selfadjoint Schrödinger operators on star-graphs with standard interface conditions ⋮ On multiplicity of eigenvalues in quantum graph theory ⋮ On extremal eigenvalues of the graph Laplacian ^*

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