Some Jacobi matrices with decaying potential and dense point spectrum
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Publication:798521
DOI10.1007/BF01218563zbMath0546.35048OpenAlexW1968003104MaRDI QIDQ798521
Publication date: 1982
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01218563
General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Difference operators (39A70)
Related Items (30)
ON THE SPECTRAL PROPERTIES OF DISCRETE SCHRÖDINGER OPERATORS ⋮ The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation ⋮ An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators ⋮ Dense point spectra of Schrödinger and Dirac operators ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ One-dimensional Schrödinger operators with random decaying potentials ⋮ One-dimensional discrete Dirac operators in a decaying random potential. I: Spectrum and dynamics ⋮ Preservation of a.c.\ spectrum for random decaying perturbations of square-summable high-order variation ⋮ On new relations between spectral properties of Jacobi matrices and their coefficients ⋮ Dynamical localization for the one-dimensional continuum Anderson model in a decaying random potential ⋮ Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square-summable variation ⋮ Schrödinger operators in the twentieth century ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach ⋮ Spectral and dynamical properties of certain random Jacobi matrices with growing parameters ⋮ Spectrum of a random Schrödinger difference operator ⋮ Unnamed Item ⋮ The spectrum of differential operators of order \(2n\) with almost constant coefficients ⋮ Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach ⋮ Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles ⋮ Generalized Prüfer variables for perturbations of Jacobi and CMV matrices ⋮ Spectral fluctuations for Schrödinger operators with a random decaying potential ⋮ Monotone Jacobi parameters and non-Szegő weights ⋮ The Kunz-Souillard approach to localization for Jacobi operators ⋮ A continuum version of the Kunz–Souillard approach to localization in one dimension ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Schrödinger operators with decaying potentials: some counterexamples ⋮ One-dimensional Schrödinger operators with random potentials: a survey ⋮ Spectral properties of random Schrödinger operators with unbounded potentials ⋮ On the point spectrum of discrete Schrödinger operator
Cites Work
- Sur le spectre des opérateurs aux différences finies aléatoires
- Singular continuous measures in scattering theory
- Scattering theory for Schrödinger operators with long-range potentials. I. Abstract theory
- A pure point spectrum of the stochastic one-dimensional Schrödinger operator
- Singular continuous spectrum for a class of almost periodic Jacobi matrices
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