Self‐adjoint and Markovian extensions of infinite quantum graphs

DOI10.1112/jlms.12539zbMath1530.81081arXiv1911.04735MaRDI QIDQ6135269

Delio Mugnolo, Noema Nicolussi, Aleksey S. Kostenko

Publication date: 24 August 2023

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

Full work available at URL: https://arxiv.org/abs/1911.04735

zbMATH Keywords

trace mapsdeficiency indicesselfadjoint extensionsKirchhoff LaplacianMarkovian extensionsfinite energy extensionsinfinite quantum graphs

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Length, area, volume, other geometric measure theory (28A75) Distance in graphs (05C12) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Signed and weighted graphs (05C22) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Operators arising in mathematical physics (47B93)

Related Items (6)

Spectral minimal partitions of unbounded metric graphs ⋮ Laplacians on infinite graphs: discrete vs. continuous ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ Gaussian Whittle-Matérn fields on metric graphs ⋮ Schrödinger and polyharmonic operators on infinite graphs: parabolic well-posedness and \(p\)-independence of spectra ⋮ On torsional rigidity and ground-state energy of compact quantum graphs

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