SINGULAR SPECTRUM FOR RADIAL TREES

DOI10.1142/S0129055X09003773zbMath1177.05069arXiv0806.0649MaRDI QIDQ3653369

Rupert L. Frank, Jonathan Breuer

Publication date: 22 December 2009

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.0649

zbMATH Keywords

Schrödinger operatorstreesquantum graphssingular spectrumreflectionless property

Mathematics Subject Classification ID

Trees (05C05) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) General spectral theory of ordinary differential operators (34L05) PDEs in connection with quantum mechanics (35Q40) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

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Cites Work

• Unnamed Item
• Unnamed Item
• Singular continuous spectrum for the Laplacian on certain sparse trees
• Absolutely continuous spectra of quantum tree graphs with weak disorder
• Singular continuous measures in scattering theory
• Spectral analysis on infinite Sierpiński gaskets
• Operators with singular continuous spectrum. I: General operators
• Geometrical aspects of spectral theory and value distribution for Herglotz functions
• Pure point spectrum of the Laplacians on fractal graphs
• The Laplacian on rapidly branching trees
• The absolutely continuous spectrum of one-dimensional Schrödinger operators
• Direct and inverse spectral theory of one-dimensional Schrödinger operators with measures
• Eigenvalue Estimates for the Weighted Laplacian on Metric Trees
• Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators
• Operators with singular continuous spectrum, V. Sparse potentials
• On the spectrum of the Laplacian on regular metric trees
• A Krein-like formula for singular perturbations of self-adjoint operators and applications
• Asymptotic value distribution for solutions of the Schrödinger equation