Essential spectrum and Weyl asymptotics for discrete Laplacians

DOI10.5802/afst.1456zbMath1342.81142arXiv1406.5391OpenAlexW2248762965MaRDI QIDQ744950

Sylvain Golénia, Michel Bonnefont

Publication date: 12 October 2015

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5391

zbMATH Keywords

Hardy inequalitydiscrete Laplaciansweakly spherically symmetric graph

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Harmonic analysis and PDEs (42B37)

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Discrete weighted Hardy inequality in 1-D ⋮ The magnetic discrete Laplacian inferred from the Gauß-Bonnet operator and application ⋮ Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature ⋮ Optimal Hardy inequalities for Schrödinger operators on graphs ⋮ Spectral analysis of the Laplacian acting on discrete cusps and funnels ⋮ The adjacency matrix and the discrete Laplacian acting on forms ⋮ Poincaré and Hardy Inequalities on Homogeneous Trees ⋮ On the essential spectrum of Schrödinger operators on trees ⋮ The discrete Laplacian acting on 2-forms and application ⋮ Discrete magnetic bottles on quasi-linear graphs ⋮ Some function theoretic properties of nonlinear resistive networks

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