Eigenfunction expansions for Schrödinger operators on metric graphs
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Publication:1030491
DOI10.1007/s00020-008-1636-zzbMath1170.47009arXiv0801.1376OpenAlexW2118315176MaRDI QIDQ1030491
Peter Stollmann, Carsten Schubert, Daniel H. Lenz
Publication date: 1 July 2009
Published in: Integral Equations and Operator Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0801.1376
Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)
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Generalized Eigenfunctions and Spectral Theory for Strongly Local Dirichlet Forms ⋮ Sch'nol's theorem for strongly local forms ⋮ Uniform existence of the integrated density of states on metric Cayley graphs ⋮ Pseudodifferential operators on periodic graphs ⋮ Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces ⋮ Localization on quantum graphs with random edge lengths ⋮ Existence of eigenvalues embedded in the spectral bands of Schrödinger operators on carbon nanotubes with impurities ⋮ Anderson localization for radial tree-like random quantum graphs ⋮ On the decomposition principle and a Persson type theorem for general regular Dirichlet forms ⋮ New relations between discrete and continuous transition operators on (metric) graphs
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