The Laplacian on rapidly branching trees

DOI10.1215/S0012-7094-96-08308-8zbMath0856.58044OpenAlexW2092517882MaRDI QIDQ1918375

Koji Fujiwara

Publication date: 24 February 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08308-8

zbMATH Keywords

eigenvalueinfinite graphcombinatorial Laplacianinfinite symmetric treerapidly branching tree

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Graph theory (05C99)

Related Items (36)

Spectral estimates for infinite quantum graphs ⋮ A spectral property of discrete Schrödinger operators with non-negative potentials ⋮ Volume growth and spectrum for general graph Laplacians ⋮ Strong isoperimetric inequalities and combinatorial curvatures on multiply connected planar graphs ⋮ The essential spectrum of the Laplacian on rapidly branching tessellations ⋮ Volume growth, spectrum and stochastic completeness of infinite graphs ⋮ Magnetic-sparseness and Schrödinger operators on graphs ⋮ Growth and the spectrum of the Laplacian of an infinite graph ⋮ Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs ⋮ Note on basic features of large time behaviour of heat kernels ⋮ Unnamed Item ⋮ Gelfand's inverse problem for the graph Laplacian ⋮ Inverse Problems for Discrete Heat Equations and Random Walks for a Class of Graphs ⋮ Cheeger constants, growth and spectrum of locally tessellating planar graphs ⋮ Localization criteria for Anderson models on locally finite graphs ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ On the \(l^p\) spectrum of Laplacians on graphs ⋮ Quantum walks induced by Dirichlet random walks on infinite trees ⋮ Curvature, geometry and spectral properties of planar graphs ⋮ Strong Isoperimetric Inequality for Tessellating Quantum Graphs ⋮ The dual Cheeger constant and spectra of infinite graphs ⋮ Sectional curvature of polygonal complexes with planar substructures ⋮ On the essential spectrum of Schrödinger operators on trees ⋮ Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians ⋮ An overview of curvature bounds and spectral theory of planar tessellations ⋮ Eigenvalue asymptotics for Schrödinger operators on sparse graphs ⋮ Intrinsic Metrics on Graphs: A Survey ⋮ Duality properties of strong isoperimetric inequalities on a planar graph and combinatorial curvatures ⋮ Essential spectrum and Weyl asymptotics for discrete Laplacians ⋮ Dirichlet \(p\)-Laplacian eigenvalues and Cheeger constants on symmetric graphs ⋮ Uniqueness for solutions of the Schrödinger equation on trees ⋮ Sectoriality and essential spectrum of non symmetric graph Laplacians ⋮ Geometry and spectrum of rapidly branching graphs ⋮ SINGULAR SPECTRUM FOR RADIAL TREES ⋮ On the decomposition principle and a Persson type theorem for general regular Dirichlet forms ⋮ Non self-adjoint Laplacians on a directed graph

Cites Work

• Pure point spectrum and negative curvature for noncompact manifolds
• On the essential spectrum of a complete Riemannian manifold
• The spectral geometry of \(k\)-regular groups
• Growth and the spectrum of the Laplacian of an infinite graph
• The spectrum of infinite regular line graphs
• Unnamed Item
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