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What is Aperiodic Order

- M. Baake, D. Damanik, U. Grimm
- Mathematics
- 24 March 2002

The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order,… Expand

The Analytic Theory of Matrix Orthogonal Polynomials

- D. Damanik, A. Pushnitski, B. Simon
- Mathematics, Economics
- 16 November 2007

We survey the analytic theory of matrix orthogonal polynomials. MSC: 42C05, 47B36, 30C10 keywords: orthogonal polynomials, matrix-valued measures, block Jacobi matrices, block CMV matrices

Uniform Spectral Properties of One-Dimensional Quasicrystals, III. α-Continuity

- D. Damanik, R. Killip, D. Lenz
- Mathematics
- 12 October 1999

Abstract: We study the spectral properties of one-dimensional whole-line Schrödinger operators, especially those with Sturmian potentials. Building upon the Jitomirskaya–Last extension of the… Expand

Perturbations of orthogonal polynomials with periodic recursion coefficients

- D. Damanik, R. Killip, B. Simon
- Mathematics
- 13 February 2007

The results of Denisov-Rakhmanov, Szegő-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to… Expand

Upper bounds in quantum dynamics

- D. Damanik, Serguei Tcheremchantsev
- Physics
- 22 February 2005

Of course, the case of main interest is where H is given by L2(Rd) or ?2(Zd), H is a Schr?dinger operator of the form ? A + V, and ip(0) is a localized wavepacket. Under the time evolution (1), the… Expand

Palindrome complexity

- J. Allouche, M. Baake, J. Cassaigne, D. Damanik
- MathematicsTheor. Comput. Sci.
- 14 June 2001

LOCALIZATION FOR ONE DIMENSIONAL, CONTINUUM, BERNOULLI-ANDERSON MODELS

- D. Damanik, Robert Sims, G. Stolz
- Mathematics
- 14 October 2000

We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of… Expand

Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian

- D. Damanik, A. Gorodetski
- Mathematics
- 3 June 2008

We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this… Expand

Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign

- D. Damanik, D. Hundertmark, R. Killip, B. Simon
- Mathematics
- 11 November 2002

AbstractLet H be a one-dimensional discrete Schrödinger operator. We prove that if Σess(H)⊂[−2,2], then H−H0 is compact and Σess(H)=[−2,2]. We also prove that if ${{H_0 + \frac 14 V^2}}$ has at least… Expand

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