On the spectrum of Schrödinger operators with a finitely supported potential on the \(d\)-regular tree

DOI10.1016/j.laa.2009.06.033zbMath1187.39002OpenAlexW1975440127MaRDI QIDQ732089

Yusuke Higuchi, Kazunori Ando

Publication date: 9 October 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.06.033

zbMATH Keywords

spectrumgraphsdiscrete Schrödinger operatorstreesdiscrete Laplacian

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Discrete version of topics in analysis (39A12) Difference operators (39A70) Linear difference operators (47B39)

Related Items (2)

On the number of discrete eigenvalues of a discrete Schrödinger operator with a finitely supported potential ⋮ Spectral and scattering theory for Schrödinger operators on perturbed topological crystals

Cites Work

• Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs
• Singular continuous spectrum for the Laplacian on certain sparse trees
• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign
• Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators.
• Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs
• Schrödinger operators with few bound states
• A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE
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