Operators with singular continuous spectrum. II: Rank one operators

DOI10.1007/BF02099737zbMath1055.47500MaRDI QIDQ1344512

Barry Simon, Rafael René del Río Castillo, Nikolai Makarov

Publication date: 3 July 1995

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

Spectrum, resolvent (47A10) General spectral theory of ordinary differential operators (34L05) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (44)

Logarithmic Quantum Dynamical Bounds for Arithmetically Defined Ergodic Schrödinger Operators with Smooth Potentials ⋮ Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy ⋮ Transfer matrices and transport for Schrödinger operators. ⋮ Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators ⋮ Fractal dimensions of spectral measures of rank one perturbations of a positive self-adjoint operator ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Continuous spectrum and uniform localization for ergodic Schrödinger operators ⋮ Spectral flow inside essential spectrum ⋮ Research on singular Sturm-Liouville spectral problems with a weighted function ⋮ Hyponormality of finite rank perturbations of normal operators ⋮ On the singular continuous spectrum of self-adjoint extensions ⋮ Rank-one perturbation of weighted shifts on a directed tree: partial normality and weak hyponormality ⋮ Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points ⋮ Operators with singular continuous spectrum. VII: Examples with borderline time decay ⋮ On typical properties of Hilbert space operators ⋮ Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials ⋮ Singular continuous spectrum is generic ⋮ Stability of spectral types of quasi-periodic Schrödinger operators with respect to perturbations by decaying potentials ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ A spectral alternative for continuous families of self-adjoint operators ⋮ Singular Integrals, Rank One Perturbations and Clark Model in General Situation ⋮ The absolutely continuous spectrum of Jacobi matrices ⋮ Boundary conditions of Sturm-Liouville operators with mixed spectra. ⋮ Absolutely continuous spectrum of Stark operators ⋮ Parametric Furstenberg theorem on random products of \(\mathrm{SL}(2, \mathbb{R})\) matrices ⋮ On the asymptotic dynamics of 2-D magnetic quantum systems ⋮ The topology of mobility-gapped insulators ⋮ One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum ⋮ Upper bounds on wavepacket spreading for random Jacobi matrices ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Extendability of eigenvalues for continuous families of self-adjoint operators ⋮ Rank-one perturbations of diagonal operators ⋮ Dimensional Hausdorff Properties of Singular Continuous Spectra ⋮ Unnamed Item ⋮ Modified Prüfer and EFGP transforms and deterministic models with dense point spectrum ⋮ On inverse spectral theory for selfadjoint extensions: Mixed types of spectra ⋮ Spectral analysis on infinite Sierpiński gaskets ⋮ Singular spectrum and recent results on hierarchical operators ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization ⋮ Anomalous Transport: A Mathematical Framework ⋮ Dimensional Hausdorff Properties of Singular Continuous Spectra ⋮ Spectral localization in the hierarchical Anderson model ⋮ Upper bounds on transport exponents for long-range operators

Cites Work

This page was built for publication: Operators with singular continuous spectrum. II: Rank one operators