Weighted Mourre's commutator theory, application to Schroedinger operators with oscillating potential

DOI10.7900/jot.2011may06.1922zbMath1289.47022arXiv1012.0705WikidataQ114010814 ScholiaQ114010814MaRDI QIDQ2857164

Sylvain Golénia, Thierry Jecko

Publication date: 31 October 2013

Published in: Journal of Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.0705

zbMATH Keywords

continuous spectrumSchrödinger operatorslimiting absorption principleMourre estimateWigner-von Neumann potentialMourre's commutator theory

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Scattering theory for PDEs (35P25) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (2)-body potential quantum scattering theory (81U05) Scattering theory of linear operators (47A40) Special quantum systems, such as solvable systems (81Q80)

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An index theorem on asymptotically static spacetimes with compact Cauchy surface ⋮ Spectral analysis of the Laplacian acting on discrete cusps and funnels ⋮ Limiting absorption principle for discrete Schrödinger operators with a Wigner-von Neumann potential and a slowly decaying potential ⋮ Bands of pure absolutely continuous spectrum for lattice Schrödinger operators with a more general long range condition ⋮ The limiting absorption principle for the discrete Wigner-von Neumann operator ⋮ Limiting absorption principle for Schrödinger operators with oscillating potentials ⋮ A remark on the Mourre theory for two body Schrödinger operators ⋮ Propagation estimates for one commutator regularity ⋮ Abstract theory of pointwise decay with applications to wave and Schrödinger equations

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