Constructive Approximation, ISSN 0176-4276, 12/2018, Volume 48, Issue 3, pp. 473 - 500

We are interested in the phenomenon of the essential spectrum instability for a class of unbounded (block) Jacobi matrices. We give a series of sufficient...

Primary: 47B36 | Secondary: 47A10 | Numerical Analysis | Analysis | Unbounded (block) Jacobi matrices | Levinson’s asymptotic theory | Mathematics | Gilbert–Pearson subordinacy theory | Instability of the essential spectrum | MATHEMATICS | Gilbert-Pearson subordinacy theory | Levinson's asymptotic theory | Unbounded (block)Jacobi matrices | SUBORDINACY | OPERATORS | ENTRIES | Spectral Theory

Primary: 47B36 | Secondary: 47A10 | Numerical Analysis | Analysis | Unbounded (block) Jacobi matrices | Levinson’s asymptotic theory | Mathematics | Gilbert–Pearson subordinacy theory | Instability of the essential spectrum | MATHEMATICS | Gilbert-Pearson subordinacy theory | Levinson's asymptotic theory | Unbounded (block)Jacobi matrices | SUBORDINACY | OPERATORS | ENTRIES | Spectral Theory

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2016, Volume 342, Issue 2, pp. 491 - 531

We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LAW | STABILITY | ASYMPTOTICS | SUBORDINACY | EIGENFUNCTIONS | SPECTRUM | PHYSICS, MATHEMATICAL | SCHRODINGER | ALTSHULER-SHKLOVSKII FORMULAS | Jewish schools | Analysis

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LAW | STABILITY | ASYMPTOTICS | SUBORDINACY | EIGENFUNCTIONS | SPECTRUM | PHYSICS, MATHEMATICAL | SCHRODINGER | ALTSHULER-SHKLOVSKII FORMULAS | Jewish schools | Analysis

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 09/2017, Volume 37, Issue 6, pp. 1681 - 1764

In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schrödinger operators whose potentials are obtained by...

Survey Article | MATHEMATICS | MATHEMATICS, APPLIED | LIMIT-PERIODIC POTENTIALS | POWER-LAW SUBORDINACY | DIMENSIONAL QUASI-CRYSTALS | RANK-ONE PERTURBATIONS | SINGULAR CONTINUOUS-SPECTRUM | TIGHT-BINDING MODEL | ABSOLUTELY CONTINUOUS-SPECTRUM | ANDERSON LOCALIZATION | DENSITY-OF-STATES | POSITIVE LYAPUNOV EXPONENTS | Operators | Orbits | Ergodic processes

Survey Article | MATHEMATICS | MATHEMATICS, APPLIED | LIMIT-PERIODIC POTENTIALS | POWER-LAW SUBORDINACY | DIMENSIONAL QUASI-CRYSTALS | RANK-ONE PERTURBATIONS | SINGULAR CONTINUOUS-SPECTRUM | TIGHT-BINDING MODEL | ABSOLUTELY CONTINUOUS-SPECTRUM | ANDERSON LOCALIZATION | DENSITY-OF-STATES | POSITIVE LYAPUNOV EXPONENTS | Operators | Orbits | Ergodic processes

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 06/2016, Volume 57, Issue 6, p. 63501

Existence of generic sets of self-adjoint operators, related to correlation dimensions of spectral measures, is investigated in separable Hilbert spaces....

SINGULAR CONTINUOUS-SPECTRUM | QUANTUM DYNAMICS | TRANSPORT | POWER-LAW SUBORDINACY | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Operators (mathematics) | Fourier transforms | Theorems | Existence theorems | Correlation analysis | Spectra | Hilbert space

SINGULAR CONTINUOUS-SPECTRUM | QUANTUM DYNAMICS | TRANSPORT | POWER-LAW SUBORDINACY | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Operators (mathematics) | Fourier transforms | Theorems | Existence theorems | Correlation analysis | Spectra | Hilbert space

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 2017, Volume 54, Issue 2, pp. 273 - 285

We show that spectral Hausdorff dimensional properties of discrete Schr "odinger operators with (1) Sturmian potentials of bounded density and (2) a class of...

MATHEMATICS | LOCALIZATION | RANK-ONE PERTURBATIONS | SINGULAR CONTINUOUS-SPECTRUM | LAW SUBORDINACY | ALPHA-CONTINUITY | LINE OPERATORS | QUASI-CRYSTALS

MATHEMATICS | LOCALIZATION | RANK-ONE PERTURBATIONS | SINGULAR CONTINUOUS-SPECTRUM | LAW SUBORDINACY | ALPHA-CONTINUITY | LINE OPERATORS | QUASI-CRYSTALS

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 1/2006, Volume 92, Issue 1, pp. 251 - 272

A family $\mathbf{A}_\alpha$ of differential operators depending on a real parameter $\alpha \ge 0$ is considered. This family was suggested by Smilansky as a...

MATHEMATICS | OPERATORS | SUBORDINACY

MATHEMATICS | OPERATORS | SUBORDINACY

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2015, Volume 56, Issue 1, p. 12701

Avila and Jitomirskaya prove that the spectral measure mu(f)(lambda nu,alpha,chi) of quasi-periodic Schrodinger operator is 1/2-Holder continuous with...

POWER-LAW SUBORDINACY | SINGULAR CONTINUOUS-SPECTRUM | INTEGRATED DENSITY | ABSOLUTELY CONTINUOUS-SPECTRUM | ANDERSON LOCALIZATION | PHYSICS, MATHEMATICAL | DENSITY-OF-STATES | Operators (mathematics) | Mathematical analysis

POWER-LAW SUBORDINACY | SINGULAR CONTINUOUS-SPECTRUM | INTEGRATED DENSITY | ABSOLUTELY CONTINUOUS-SPECTRUM | ANDERSON LOCALIZATION | PHYSICS, MATHEMATICAL | DENSITY-OF-STATES | Operators (mathematics) | Mathematical analysis

Journal Article

Analysis and PDE, ISSN 2157-5045, 2018, Volume 12, Issue 4, pp. 867 - 892

We show that positive Lyapunov exponents imply upper quantum dynamical bounds for Schrodinger operators H-f,(theta) u(n) = u(n + 1) u(n - 1) + empty set (f (n)...

Skew-shift | Transport exponent | Multifrequency quasiperiodic | MATHEMATICS | LOCALIZATION | MATHEMATICS, APPLIED | transport exponent | POWER-LAW SUBORDINACY | multifrequency quasiperiodic | SINGULAR CONTINUOUS-SPECTRUM | LINE OPERATORS | skew-shift | SCHRODINGER-OPERATORS

Skew-shift | Transport exponent | Multifrequency quasiperiodic | MATHEMATICS | LOCALIZATION | MATHEMATICS, APPLIED | transport exponent | POWER-LAW SUBORDINACY | multifrequency quasiperiodic | SINGULAR CONTINUOUS-SPECTRUM | LINE OPERATORS | skew-shift | SCHRODINGER-OPERATORS

Journal Article

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Full Text
Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

Journal of Difference Equations and Applications, ISSN 1023-6198, 08/2018, Volume 24, Issue 8, pp. 1247 - 1272

We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do...

periodic operators | Jacobi matrices | embedded eigenvalues | spectral theory | Wigner-von Neumann | MATHEMATICS, APPLIED | HETEROSTRUCTURES | SUBORDINACY | POTENTIALS | BOUND-STATES | MATRICES | CONTINUUM | SPECTRUM | SCHRODINGER-OPERATORS | Eigenvalues | Embedding | Operators | Dependence

periodic operators | Jacobi matrices | embedded eigenvalues | spectral theory | Wigner-von Neumann | MATHEMATICS, APPLIED | HETEROSTRUCTURES | SUBORDINACY | POTENTIALS | BOUND-STATES | MATRICES | CONTINUUM | SPECTRUM | SCHRODINGER-OPERATORS | Eigenvalues | Embedding | Operators | Dependence

Journal Article

Studia Mathematica, ISSN 0039-3223, 2018, Volume 242, Issue 2, pp. 179 - 215

For an arbitrary Hermitian period-T Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the...

Jacobi operators | Subordinate solutions | Periodic operators | Levinson techniques | Wigner-von Neumann potentials | PERTURBATIONS | DIMENSIONAL SCHRODINGER-OPERATORS | SUBORDINACY | POTENTIALS | periodic operators | DENSITY | MATHEMATICS | SYSTEMS | subordinate solutions | ZEROS

Jacobi operators | Subordinate solutions | Periodic operators | Levinson techniques | Wigner-von Neumann potentials | PERTURBATIONS | DIMENSIONAL SCHRODINGER-OPERATORS | SUBORDINACY | POTENTIALS | periodic operators | DENSITY | MATHEMATICS | SYSTEMS | subordinate solutions | ZEROS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 07/2011, Volume 52, Issue 7, pp. 073501 - 073501-21

We study spectral properties of some discrete Dirac operators with nonzero potential only at some sparse and suitably randomly distributed positions. As...

HAUSDORFF DIMENSION | SINGULAR CONTINUOUS-SPECTRUM | SUBORDINACY | JACOBI MATRICES | POTENTIALS | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

HAUSDORFF DIMENSION | SINGULAR CONTINUOUS-SPECTRUM | SUBORDINACY | JACOBI MATRICES | POTENTIALS | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 03/2015, Volume 191, pp. 71 - 93

We explore the spectral theory of the orthogonal polynomials associated to the classical Cantor measure and similar singular continuous measures. We prove...

Cantor set | Orthogonal polynomials | Almost periodic | 26A30 | 58J53 | 42C05 | JULIA SETS | MATHEMATICS | POWER-LAW SUBORDINACY | FINE-STRUCTURE | BEHAVIOR | LINE OPERATORS | JACOBI MATRICES | SINGULAR SPECTRA | ZEROS

Cantor set | Orthogonal polynomials | Almost periodic | 26A30 | 58J53 | 42C05 | JULIA SETS | MATHEMATICS | POWER-LAW SUBORDINACY | FINE-STRUCTURE | BEHAVIOR | LINE OPERATORS | JACOBI MATRICES | SINGULAR SPECTRA | ZEROS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 7/2016, Volume 85, Issue 3, pp. 427 - 450

The Wigner-von Neumann method, which has previously been used for perturbing continuous Schrödinger operators, is here applied to their discrete counterparts....

Mathematics | Wigner-von Neumann potential | Subordinate solutions | Spectral theory | Analysis | Periodic Jacobi operators | DENSE POINT SPECTRUM | MATHEMATICS | DIMENSIONAL SCHRODINGER-OPERATORS | SYSTEMS | SUBORDINACY | POTENTIALS

Mathematics | Wigner-von Neumann potential | Subordinate solutions | Spectral theory | Analysis | Periodic Jacobi operators | DENSE POINT SPECTRUM | MATHEMATICS | DIMENSIONAL SCHRODINGER-OPERATORS | SYSTEMS | SUBORDINACY | POTENTIALS

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 3/2017, Volume 166, Issue 6, pp. 1509 - 1557

It is well known that, an energy is in the spectrum of Fibonacci Hamiltonian if and only if the corresponding trace orbit is bounded. However, it is not known...

Physical Chemistry | Thue–Morse Hamiltonian | Local Hausdorff dimension | Theoretical, Mathematical and Computational Physics | Subordinate solution | Quantum Physics | Pseudo localization | Trace orbit | Physics | Statistical Physics and Dynamical Systems | LOCALIZATION | POWER-LAW SUBORDINACY | Thue-Morse Hamiltonian | DIMENSIONAL SCHRODINGER-OPERATORS | SINGULAR CONTINUOUS-SPECTRUM | PHYSICS, MATHEMATICAL | CONTROLLED DISORDER | EXTENDED STATES | TRANSFER-MATRICES | LINE OPERATORS | QUASI-CRYSTALS | MEASURE ZERO

Physical Chemistry | Thue–Morse Hamiltonian | Local Hausdorff dimension | Theoretical, Mathematical and Computational Physics | Subordinate solution | Quantum Physics | Pseudo localization | Trace orbit | Physics | Statistical Physics and Dynamical Systems | LOCALIZATION | POWER-LAW SUBORDINACY | Thue-Morse Hamiltonian | DIMENSIONAL SCHRODINGER-OPERATORS | SINGULAR CONTINUOUS-SPECTRUM | PHYSICS, MATHEMATICAL | CONTROLLED DISORDER | EXTENDED STATES | TRANSFER-MATRICES | LINE OPERATORS | QUASI-CRYSTALS | MEASURE ZERO

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 04/2008, Volume 61, Issue 4, pp. 486 - 538

We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and...

DENSITY | MATHEMATICS | MATHEMATICS, APPLIED | POWER-LAW SUBORDINACY | MATRICES | ASYMPTOTICS | PERIODIC SCHRODINGER-OPERATORS | SINGULAR SPECTRA

DENSITY | MATHEMATICS | MATHEMATICS, APPLIED | POWER-LAW SUBORDINACY | MATRICES | ASYMPTOTICS | PERIODIC SCHRODINGER-OPERATORS | SINGULAR SPECTRA

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 02/2010, Volume 53, Issue 1, pp. 239 - 254

We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic (‘double root’) situation. For the model with ‘non-smooth’...

subordinacy theory | Jacobi matrices | asymptotics of generalized eigenvectors | MATHEMATICS | ASYMPTOTIC ANALYSIS | SYSTEMS | SUBORDINACY | OPERATORS | Mathematical analysis | Asymptotic methods | Matrix | Mathematics - Spectral Theory

subordinacy theory | Jacobi matrices | asymptotics of generalized eigenvectors | MATHEMATICS | ASYMPTOTIC ANALYSIS | SYSTEMS | SUBORDINACY | OPERATORS | Mathematical analysis | Asymptotic methods | Matrix | Mathematics - Spectral Theory

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 05/1998, Volume 194, Issue 1, pp. 1 - 45

Using control of the growth of the transfer matrices, wediscuss the spectral analysis of continuum and discrete half-line Schrödinger operators with slowly...

SINGULAR CONTINUOUS-SPECTRUM | PURE POINT | SUBORDINACY | PHYSICS, MATHEMATICAL | DETERMINISTIC POTENTIALS

SINGULAR CONTINUOUS-SPECTRUM | PURE POINT | SUBORDINACY | PHYSICS, MATHEMATICAL | DETERMINISTIC POTENTIALS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 368, Issue 1, pp. 218 - 234

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any...

Sparse potentials | Hausdorff dimension | Spectral measure | Block-Jacobi matrices | MATHEMATICS | MATHEMATICS, APPLIED | TREES | SINGULAR CONTINUOUS-SPECTRUM | SUBORDINACY | POTENTIALS | SCHRODINGER-OPERATORS

Sparse potentials | Hausdorff dimension | Spectral measure | Block-Jacobi matrices | MATHEMATICS | MATHEMATICS, APPLIED | TREES | SINGULAR CONTINUOUS-SPECTRUM | SUBORDINACY | POTENTIALS | SCHRODINGER-OPERATORS

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 06/2014, Volume 144, Issue 3, pp. 533 - 555

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real,...

DENSE POINT SPECTRUM | MATHEMATICS | MATHEMATICS, APPLIED | SUBORDINACY | DECAYING POTENTIALS | DIMENSIONAL SCHRODINGER-OPERATORS | Mathematics | Differential equations | Operators | Scattering | Angular momentum | Proving | Spectra | Coefficients | Estimates | Constraining

DENSE POINT SPECTRUM | MATHEMATICS | MATHEMATICS, APPLIED | SUBORDINACY | DECAYING POTENTIALS | DIMENSIONAL SCHRODINGER-OPERATORS | Mathematics | Differential equations | Operators | Scattering | Angular momentum | Proving | Spectra | Coefficients | Estimates | Constraining

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2015, Volume 105, Issue 11, pp. 1479 - 1497

The spectra of massless Dirac operators are of essential interest, e.g., for the electronic properties of graphene, but fundamental questions such as the...

Geometry | Theoretical, Mathematical and Computational Physics | massless Dirac operators | Group Theory and Generalizations | embedded eigenvalues | 81Q10 | Statistical Physics, Dynamical Systems and Complexity | 35Q40 | Physics | 47F05 | scalar potentials | graphene | INFINITY | DIRICHLET FORMS | SYSTEMS | SUBORDINACY | ABSOLUTELY CONTINUOUS-SPECTRUM | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Graphene | Analysis | Mathematics - Spectral Theory

Geometry | Theoretical, Mathematical and Computational Physics | massless Dirac operators | Group Theory and Generalizations | embedded eigenvalues | 81Q10 | Statistical Physics, Dynamical Systems and Complexity | 35Q40 | Physics | 47F05 | scalar potentials | graphene | INFINITY | DIRICHLET FORMS | SYSTEMS | SUBORDINACY | ABSOLUTELY CONTINUOUS-SPECTRUM | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Graphene | Analysis | Mathematics - Spectral Theory

Journal Article

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