Power-law subordinacy and singular spectra. I: Half-line operators
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Publication:1588923
DOI10.1007/BF02392827zbMath0991.81021OpenAlexW2331222876WikidataQ56005115 ScholiaQ56005115MaRDI QIDQ1588923
Yoram Last, Svetlana Ya. Jitomirskaya
Publication date: 6 December 2000
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392827
generalized Gilbert Pearson analysisoperators with singular continuous spectrumspectral decomposition with respect to the spectral Hausdorff dimension
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Difference operators (39A70) Linear difference operators (47B39)
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Cites Work
- The analysis of additive set functions in Euclidean space
- On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
- Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
- Power law subordinacy and singular spectra. II: Line operators.
- One-dimensional Schrödinger operator with unbounded potential: The pure point spectrum
- Trace class perturbations and the absence of absolutely continuous spectra
- Operators with singular continuous spectrum. VII: Examples with borderline time decay
- Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains
- Deterministic potential with a pure point spectrum
- Additive set functions in Euclidean space. II
- Quantum dynamics and decompositions of singular continuous spectra
- Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
- Schrödinger semigroups
- On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
- Dimensional Hausdorff Properties of Singular Continuous Spectra
- LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
- Operators with singular continuous spectrum, V. Sparse potentials
- Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
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