Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures

DOI10.1016/j.jmaa.2012.07.005zbMath1260.47010arXiv1109.0712OpenAlexW2069037148MaRDI QIDQ714079

Konstantin Pankrashkin

Publication date: 19 October 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.0712

zbMATH Keywords

Weyl functionmetric graphquantum graphboundary tripletselfadjoint extension

Mathematics Subject Classification ID

Dilations, extensions, compressions of linear operators (47A20) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (16)

Spectral estimates for infinite quantum graphs ⋮ Continuum limit of the lattice quantum graph Hamiltonian ⋮ Laplacians on infinite graphs: discrete vs. continuous ⋮ Magnetic square lattice with vertex coupling of a preferred orientation ⋮ An example of unitary equivalence between self-adjoint extensions and their parameters ⋮ A remark on the discriminant of Hill's equation and Herglotz functions ⋮ Non-compact quantum graphs with summable matrix potentials ⋮ Scattering on periodic metric graphs ⋮ Spectral theory of infinite quantum graphs ⋮ Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees ⋮ Schrödinger and polyharmonic operators on infinite graphs: parabolic well-posedness and \(p\)-independence of spectra ⋮ On the Spectra of Schrödinger Operators on Zigzag Nanotubes with Multiple Bonds ⋮ Cantor spectrum of graphene in magnetic fields ⋮ Cantor spectra of magnetic chain graphs ⋮ New relations between discrete and continuous transition operators on (metric) graphs ⋮ Honeycomb structures in magnetic fields

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