The absolutely continuous spectrum of Jacobi matrices
From MaRDI portal
Publication:640782
DOI10.4007/annals.2011.174.1.4zbMath1235.47032arXiv0706.1101OpenAlexW2962930293MaRDI QIDQ640782
Publication date: 20 October 2011
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0706.1101
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Cites Work
- Unnamed Item
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- Unnamed Item
- On isospectral sets of Jacobi operators
- Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs
- Spectral properties of a class of reflectionless Schrödinger operators
- Cartan decomposition of the moment map
- Perturbations of orthogonal polynomials with periodic recursion coefficients
- One-dimensional Schrödinger operators with random decaying potentials
- Singular continuous measures in scattering theory
- The spectrum of difference operators and algebraic curves
- The spectrum of Jacobi matrices
- The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
- The classical moment problem as a self-adjoint finite difference operator
- Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
- Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
- Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
- Spectral theory for slowly oscillating potentials. I: Jacobi matrices
- Operators with singular continuous spectrum. II: Rank one operators
- Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators
- A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials
- Sparse potentials with fractional Hausdorff dimension.
- On the inverse scattering problem for Jacobi matrices with the spectrum on an interval, a finite system of intervals or a Cantor set of positive length
- The trace formula for Schrödinger operators on the line
- Trace class perturbations and the absence of absolutely continuous spectra
- Operators with singular continuous spectrum. I: General operators
- Geometrical aspects of spectral theory and value distribution for Herglotz functions
- Singular continuous spectrum for palindromic Schrödinger operators
- Pure point spectrum under 1-parameter perturbations and instability of Anderson localization
- Generalized Floquet theory for stationary Schrödinger operators in one dimension
- The essential spectrum of Schrödinger, Jacobi, and CMV operators
- On exponential representation of analytic functions in the upper half- plane with positive imaginary part
- A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part
- JACOBI MATRICES WITH RANDOM POTENTIALS TAKING FINITELY MANY VALUES
- Variation on a theme of Jacobi
- Scattering Theory and Polynomials Orthogonal on the Real Line
- Quasitriangular Matrices
- Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies
- Embedded singular continuous spectrum for one-dimensional Schrödinger operators
- Value Distribution and Spectral Theory
- Value distribution and spectral analysis of differential operators
- On Rakhmanov’s theorem for Jacobi matrices
- LOCALIZATIONS AT INFINITY AND ESSENTIAL SPECTRUM OF QUANTUM HAMILTONIANS I: GENERAL THEORY
- Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
- Asymptotic value distribution for solutions of the Schrödinger equation
- Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators
- Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure.
