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Constructive Approximation, ISSN 0176-4276, 12/2018, Volume 48, Issue 3, pp. 473 - 500
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 3/2016, Volume 342, Issue 2, pp. 491 - 531
Journal Article
Ergodic theory and dynamical systems, ISSN 0143-3857, 09/2017, Volume 37, Issue 6, pp. 1681 - 1764
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
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
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
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
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
Journal Article
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
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
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
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
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
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 3/2017, Volume 166, Issue 6, pp. 1509 - 1557
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
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
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
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
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
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 11/2015, Volume 105, Issue 11, pp. 1479 - 1497
Journal Article
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