Essential spectrum of the discrete Laplacian on a perturbed periodic graph

DOI10.1016/j.jmaa.2016.09.063zbMath1348.05128arXiv1509.09000OpenAlexW2963497944MaRDI QIDQ333925

Itaru Sasaki, Akito Suzuki

Publication date: 31 October 2016

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

Full work available at URL: https://arxiv.org/abs/1509.09000

zbMATH Keywords

perturbation theoryessential spectruminfinite graphrandom graphdiscrete Laplacianpendant

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Infinite graphs (05C63)

Related Items (11)

Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals ⋮ Spectral and scattering theory for Schrödinger operators on perturbed topological crystals ⋮ A constructive approach to topological invariants for one-dimensional strictly local operators ⋮ An index theorem for one-dimensional gapless non-unitary quantum walks ⋮ Spectral estimates for Schrödinger operators on periodic discrete graphs ⋮ The essential spectrum of the discrete Laplacian on Klaus-sparse graphs ⋮ Scattering on periodic metric graphs ⋮ Exterior diffraction problems for two-dimensional square lattice ⋮ Laplacians on periodic graphs with guides ⋮ Eigenvalues of periodic difference operators on lattice octants ⋮ Spectral and scattering theory for topological crystals perturbed by infinitely many new edges

Cites Work

• Unnamed Item
• Generator of an abstract quantum walk
• Inverse problems, trace formulae for discrete Schrödinger operators
• Spectral and asymptotic properties of Grover walks on crystal lattices
• Spectral properties of Schrödinger operators on perturbed lattices
• Inverse scattering at a fixed energy for discrete Schrödinger operators on the square lattice
• Spectra of Schrödinger operators on equilateral quantum graphs
• Spectral structure of the Laplacian on a covering graph
• The spectrum of an infinite graph
• Asymptotic behavior of the transition probability of a random walk on an infinite graph
• The spectrum of the continuous Laplacian on a graph
• Inverse scattering theory for discrete Schrödinger operators on the hexagonal lattice
• Schrödinger operators on periodic discrete graphs
• Spectrum of the Laplacian on a covering graph with pendant edges. I: The one-dimensional lattice and beyond
• Spectral mapping theorem of an abstract quantum walk
• Modified wave operators for discrete Schrödinger operators with long-range perturbations
• Note on the spectrum of discrete Schr\"odinger operators
• A Survey on Spectra of infinite Graphs
• Discrete Schrödinger operators on a graph
• SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3
• Spectral estimates for Schrödinger operators on periodic discrete graphs
• Essential spectra of difference operators on -periodic graphs

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