Spectral averaging, perturbation of singular spectra, and localization

DOI10.1090/S0002-9947-96-01579-6zbMath0868.35081OpenAlexW1728468063MaRDI QIDQ5691025

Eric Mourre, Jean-Michel Combes, Peter D. Hislop

Publication date: 9 January 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01579-6

zbMATH Keywords

random Schrödinger operatorsdifferential inequalitiesspectral averagingaveraged spectral measure

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

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Cites Work

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• On a theorem of Carey and Pincus
• Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
• Perturbation theory of dense point spectra
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Localization for some continuous random Schrödinger operators
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
• Singular continuous spectrum is generic