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## Damanik, David

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 Author ID: damanik.david Published as: Damanik, David; Damanik, D.
 Documents Indexed: 142 Publications since 1997
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#### Co-Authors

 19 single-authored 18 Gorodetskii, Anton Semenovich 16 Lenz, Daniel H. 15 Fillman, Jake 10 Lukic, Milivoje 9 Killip, Rowan 8 Goldstein, Michael 8 Simon, Barry 7 Tcheremchantsev, Serguei 7 Yessen, William N. 6 Avila Cordeiro de Melo, Artur 6 Stolz, Gunter 5 Gan, Zheng 4 Baake, Michael 4 Sukhtaiev, Selim 3 Boshernitzan, Michael D. 3 Fang, Licheng 3 Grimm, Uwe 3 Hundertmark, Dirk 3 Krüger, Helge 3 Sims, Robert L. 3 VandenBoom, Tom 3 Wang, Fengpeng 3 Zhang, Zhenghe 2 Binder, Ilia A. 2 Bochi, Jairo 2 Bucaj, Valmir 2 Embree, Mark 2 Gerbuz, Vitaly 2 Gesztesy, Fritz 2 Jitomirskaya, Svetlana Yakovlevna 2 Johnson, Russell Allan 2 Munger, Paul E. 2 Solomyak, Boris 2 Yuditskii, Peter Meerovich 1 Adamczewski, Boris 1 Adiceam, Faustin 1 Allouche, Jean-Paul Simon 1 Avron, Joseph E. 1 Berthé, Valérie 1 Bjerklöv, Kristian 1 Breuer, Jonathan 1 Cassaigne, Julien 1 Chaika, Jonathan 1 del Río Castillo, Rafael René 1 Erickson, Jon 1 Gähler, Franz 1 Ghez, Jean-Michel 1 Guo, Shuzheng 1 Haynes, Alan K. 1 Helman, Mark 1 Hinkle, Gerhardt 1 Julien, Antoine 1 Jun, Hyunkyu 1 Kellendonk, Johannes 1 Kesten, Jacob 1 Landrigan, Michael 1 Last, Yoram 1 Lemm, Marius 1 Liu, Qinghui 1 Martínez-Finkelshtein, Andrei 1 Naboko, Serguei N. 1 Navas, Andrés 1 Ong, Darren C. 1 Pushnitski, Alexander B. 1 Qu, Yanhui 1 Raymond, Laurent 1 Remling, Christian 1 Sadun, Lorenzo A. 1 Schlag, Wilhelm 1 Sütő, András 1 Teschl, Gerald 1 Vance, Robert 1 Voda, Mircea 1 Vu, Alan 1 Weiss, Barak 1 Zamboni, Luca Quardo 1 Zare, Douglas
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#### Serials

 15 Communications in Mathematical Physics 14 Journal of Functional Analysis 8 Annales Henri Poincaré 8 Oberwolfach Reports 7 Duke Mathematical Journal 6 Journal of Approximation Theory 4 Letters in Mathematical Physics 4 Inventiones Mathematicae 4 Proceedings of the American Mathematical Society 4 Journal of Spectral Theory 3 Journal d’Analyse Mathématique 3 Journal of Mathematical Analysis and Applications 3 Transactions of the American Mathematical Society 3 IMRN. International Mathematics Research Notices 2 Israel Journal of Mathematics 2 Advances in Mathematics 2 Mathematische Annalen 2 European Journal of Combinatorics 2 Journal of the American Mathematical Society 2 Forum Mathematicum 2 Geometric and Functional Analysis. GAFA 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Notices of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Journal of the European Mathematical Society (JEMS) 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Helvetica Physica Acta 1 Journal of Statistical Physics 1 Nonlinearity 1 Reviews in Mathematical Physics 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Publications Mathématiques 1 Journal of Differential Equations 1 Journal für die Reine und Angewandte Mathematik 1 Theoretical Computer Science 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Ergodic Theory and Dynamical Systems 1 Discrete & Computational Geometry 1 Electronic Journal of Differential Equations (EJDE) 1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Communications on Pure and Applied Analysis 1 Surveys in Approximation Theory (SAT) 1 Journal of Modern Dynamics 1 Electronic Research Announcements in Mathematical Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Fractal Geometry 1 Arnold Mathematical Journal
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#### Fields

 81 Operator theory (47-XX) 68 Quantum theory (81-XX) 43 Dynamical systems and ergodic theory (37-XX) 32 Statistical mechanics, structure of matter (82-XX) 31 Ordinary differential equations (34-XX) 28 Partial differential equations (35-XX) 19 Difference and functional equations (39-XX) 8 General and overarching topics; collections (00-XX) 7 Number theory (11-XX) 7 Measure and integration (28-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Convex and discrete geometry (52-XX) 7 Computer science (68-XX) 5 Special functions (33-XX) 5 Probability theory and stochastic processes (60-XX) 4 Combinatorics (05-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX)

#### Citations contained in zbMATH Open

123 Publications have been cited 1,613 times in 697 Documents Cited by Year
The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097
Damanik, David; Pushnitski, Alexander; Simon, Barry
2008
Palindrome complexity. Zbl 1064.68074
Allouche, Jean-Paul; Baake, Michael; Cassaigne, Julien; Damanik, David
2003
Uniform spectral properties of one-dimensional quasicrystals. III: $$\alpha$$-continuity. Zbl 1045.81024
Damanik, David; Killip, Rowan; Lenz, Daniel
2000
Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031
Damanik, David; Killip, Rowan; Simon, Barry
2010
Localization for one-dimensional, continuum, Bernoulli-Anderson models. Zbl 1107.82025
Damanik, David; Sims, Robert; Stolz, Günter
2002
Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues. Zbl 0962.81012
Damanik, David; Lenz, Daniel
1999
Multi-scale analysis implies strong dynamical localization. Zbl 0976.60064
Damanik, D.; Stollmann, P.
2001
The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151
Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S.
2008
Schrödinger operators with dynamically defined potentials. Zbl 06823048
Damanik, David
2017
Gordon-type arguments in the spectral theory of one-dimensional quasicrystals. Zbl 0989.81025
Damanik, David
2000
The index of Sturmian sequences. Zbl 1002.11020
Damanik, David; Lenz, Daniel
2002
Power-law bounds on transfer matrices and quantum dynamics in one dimension. Zbl 1033.81032
Damanik, David; Tcheremchantsev, Serguei
2003
Upper bounds in quantum dynamics. Zbl 1114.81036
Damanik, David; Tcheremchantsev, Serguei
2007
Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016
Damanik, David; Gorodetski, Anton
2011
A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009
Damanik, David; Lenz, Daniel
2006
Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031
Damanik, David; Embree, Mark; Gorodetski, Anton
2015
Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312
Damanik, David; Gorodetski, Anton
2009
The Fibonacci Hamiltonian. Zbl 1359.81108
Damanik, David; Gorodetski, Anton; Yessen, William
2016
Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029
Damanik, David; Simon, Barry
2006
Uniform spectral properties of one-dimensional quasicrystals. II: The Lyapunov exponent. Zbl 1044.81036
Damanik, David; Lenz, Daniel
1999
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027
Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B.
2003
$$\alpha$$-continuity properties of one-dimensional quasicrystals. Zbl 0907.34073
Damanik, David
1998
Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018
Damanik, David
2007
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030
Damanik, David; Simon, Barry
2006
Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems. Zbl 1332.82027
Damanik, David; Lukic, Milivoje; Yessen, William
2015
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Power-law bounds on transfer matrices and quantum dynamics in one dimension. II. Zbl 1059.81055
Damanik, David; Sütő, András; Tcheremchantsev, Serguei
2004
Half-line Schrödinger operators with no bound states. Zbl 1081.47027
Damanik, David; Killip, R. Rowan
2004
On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168
Damanik, David; Goldstein, Michael
2014
Strictly ergodic subshifts and associated operators. Zbl 1130.82017
Damanik, David
2007
Dynamics of unitary operators. Zbl 1321.47076
Damanik, David; Fillman, Jake; Vance, Robert
2014
Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028
Damanik, David; Lenz, Daniel
2006
Local symmetries in the period-doubling sequence. Zbl 0943.68127
Damanik, David
2000
Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010
Damanik, David; Munger, Paul; Yessen, William N.
2013
A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085
Damanik, David; Tcheremchantsev, Serguei
2010
Lower transport bounds for one-dimensional continuum Schrödinger operators. Zbl 1116.34066
Damanik, David; Lenz, Daniel; Stolz, Günter
2006
Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032
Damanik, David; Hundertmark, Dirk; Simon, Barry
2003
Powers in Sturmian sequences. Zbl 1030.68068
Damanik, David; Lenz, Daniel
2003
Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. I: The essential support of the measure. Zbl 1283.33005
Damanik, David; Munger, Paul; Yessen, William N.
2013
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data. Zbl 1342.35300
Damanik, David; Goldstein, Michael
2016
Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices. Zbl 1332.81066
Damanik, David; Fillman, Jake; Ong, Darren C.
2016
Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. Zbl 1132.81018
Damanik, David; Tcheremchantsev, Serguei
2006
Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117
Damanik, David; Gorodetski, Anton; Solomyak, Boris
2015
Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023
Damanik, David; Gan, Zheng
2011
Singular continuous spectrum for a class of substitution Hamiltonians. Zbl 0930.11007
Damanik, David
1998
Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053
Damanik, David; Gan, Zheng
2011
Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian. Zbl 1153.81011
Damanik, David; Tcheremchantsev, Serguei
2008
Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007
Damanik, David; Lenz, Daniel
2006
Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent. Zbl 1422.35022
Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; Vandenboom, Tom; Wang, Fengpeng; Zhang, Zhenghe
2019
Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016
Boshernitzan, Michael; Damanik, David
2008
Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Zbl 1081.81521
Damanik, D.; Zamboni, Luca Q.
2003
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
Dynamical upper bounds for one-dimensional quasicrystals. Zbl 1077.81039
Damanik, David
2005
Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077
Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David
2016
Palindrome complexity bounds for primitive substitution sequences. Zbl 0962.68141
Damanik, David; Zare, Douglas
2000
The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035
Damanik, David; Gorodetski, Anton
2012
Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325
Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje
2018
The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009
Damanik, David; Gorodetski, Anton
2009
Schrödinger operators with few bound states. Zbl 1082.47029
Damanik, David; Killip, Rowan; Simon, Barry
2005
Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052
Damanik, David; Fillman, Jake; Gorodetski, Anton
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113
Damanik, David; Fillman, Jake; Lukic, Milivoje
2017
Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058
Damanik, David; Gan, Zheng
2010
An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators. Zbl 1344.47021
Damanik, David; Gorodetski, Anton
2016
The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2016
Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075
Damanik, David; Killip, Rowan; Simon, Barry
2004
The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2017
Substitution Hamiltonians with bounded trace map orbits. Zbl 0996.37011
Damanik, David
2000
Schrödinger operators with many bound states. Zbl 1114.34065
Damanik, David; Remling, Christian
2007
Linear repetitivity. I: Uniform subadditive ergodic theorems and applications. Zbl 1182.37020
Damanik, D.; Lenz, D.
2001
A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians. Zbl 1092.81519
Damanik, D.; Ghez, J.-M.; Raymond, L.
2001
A version of Gordon’s theorem for multi-dimensional Schrödinger operators. Zbl 1062.47038
Damanik, David
2004
Ergodic potentials with a discontinuous sampling function are non-deterministic. Zbl 1090.47021
Damanik, David; Killip, Rowan
2005
Linearly recurrent circle map subshifts and an application to Schrödinger operators. Zbl 1023.47019
2002
Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059
Damanik, David; Gorodetski, Anton
2013
Singular continuous spectrum for a class of substitution Hamiltonians. II. Zbl 1044.81035
Damanik, David
2000
Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure. Zbl 0907.34074
Damanik, David
1998
Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials. Zbl 1173.81315
Damanik, David; Lenz, Daniel
2003
Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002
Damanik, David; Lenz, Daniel
2007
Localization for discrete one-dimensional random word models. Zbl 1043.47032
Damanik, David; Sims, Robert; Stolz, Günter
2004
Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037
Damanik, David; Yuditskii, Peter
2016
Uniform singular continuous spectrum for the period doubling Hamiltonian. Zbl 1002.47015
Damanik, David
2001
Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038
Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui
2015
Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model. Zbl 1325.33007
Damanik, David; Fillman, Jake; Lukic, Milivoje; Yessen, William
2015
Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564
Damanik, David; Fillman, Jake
2019
Some high-complexity Hamiltonians with purely singular continuous spectrum. Zbl 1021.34074
Damanik, D.; Solomyak, B.
2002
On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009
Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William
2016
A continuum version of the Kunz-Souillard approach to localization in one dimension. Zbl 1245.34084
Damanik, David; Stolz, Günter
2011
Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line. Zbl 1342.82120
Damanik, David; Erickson, Jon; Fillman, Jake; Hinkle, Gerhardt; Vu, Alan
2016
Schrödinger operators defined by interval-exchange transformations. Zbl 1184.81056
Chaika, Jon; Damanik, David; Krüger, Helge
2009
Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020
Damanik, David; Naboko, Serguei
2007
Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 06991338
Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2018
A generalization of Gordon’s theorem and applications to quasiperiodic Schrödinger operators. Zbl 0954.34074
Damanik, David; Stolz, Günter
2000
Lyapunov exponents in continuum Bernoulli-Anderson models. Zbl 1038.34049
Damanik, David; Sims, Robert; Stolz, Günter
2002
A multi-scale analysis scheme on abelian groups with an application to operators dual to Hill’s equation. Zbl 1355.35053
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2017
What is $$\ldots$$ aperiodic order? Zbl 1352.52028
Baake, Michael; Damanik, David; Grimm, Uwe
2016
From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037
Gesztesy, Fritz (ed.); Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei
2016
The repetition property for sequences on tori generated by polynomials or skew-shifts. Zbl 1186.37018
Boshernitzan, Michael; Damanik, David
2009
Localization for Anderson models on metric and discrete tree graphs. Zbl 1436.05027
Damanik, David; Fillman, Jake; Sukhtaiev, Selim
2020
Zero measure and singular continuous spectra for quantum graphs. Zbl 1442.05124
Damanik, David; Fang, Licheng; Sukhtaiev, Selim
2020
Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent. Zbl 1422.35022
Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; Vandenboom, Tom; Wang, Fengpeng; Zhang, Zhenghe
2019
Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564
Damanik, David; Fillman, Jake
2019
Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly. Zbl 07104056
Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; VandenBoom, Tom; Wang, Fengpeng; Zhang, Zhenghe
2019
Anderson localization for quasi-periodic CMV matrices and quantum walks. Zbl 1462.35316
Wang, Fengpeng; Damanik, David
2019
Anderson localization for radial tree graphs with random branching numbers. Zbl 07063145
Damanik, David; Sukhtaiev, Selim
2019
Multidimensional almost-periodic Schrödinger operators with Cantor spectrum. Zbl 07044362
Damanik, David; Fillman, Jake; Gorodetski, Anton
2019
Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325
Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje
2018
Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 06991338
Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2018
Almost periodicity in time of solutions of the Toda lattice. Zbl 1396.37067
Binder, Ilia; Damanik, David; Lukic, Milivoje; VandenBoom, Tom
2018
Spectral transitions for the square Fibonacci Hamiltonian. Zbl 06979900
Damanik, David; Gorodetski, Anton
2018
Schrödinger operators with dynamically defined potentials. Zbl 06823048
Damanik, David
2017
Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113
Damanik, David; Fillman, Jake; Lukic, Milivoje
2017
The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2017
A multi-scale analysis scheme on abelian groups with an application to operators dual to Hill’s equation. Zbl 1355.35053
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2017
The Fibonacci Hamiltonian. Zbl 1359.81108
Damanik, David; Gorodetski, Anton; Yessen, William
2016
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data. Zbl 1342.35300
Damanik, David; Goldstein, Michael
2016
Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices. Zbl 1332.81066
Damanik, David; Fillman, Jake; Ong, Darren C.
2016
Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077
Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David
2016
An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators. Zbl 1344.47021
Damanik, David; Gorodetski, Anton
2016
The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067
Damanik, David; Goldstein, Michael; Lukic, Milivoje
2016
Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037
Damanik, David; Yuditskii, Peter
2016
On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009
Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William
2016
Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line. Zbl 1342.82120
Damanik, David; Erickson, Jon; Fillman, Jake; Hinkle, Gerhardt; Vu, Alan
2016
What is $$\ldots$$ aperiodic order? Zbl 1352.52028
Baake, Michael; Damanik, David; Grimm, Uwe
2016
From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037
Gesztesy, Fritz; Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei
2016
Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031
Damanik, David; Embree, Mark; Gorodetski, Anton
2015
Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems. Zbl 1332.82027
Damanik, David; Lukic, Milivoje; Yessen, William
2015
Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117
Damanik, David; Gorodetski, Anton; Solomyak, Boris
2015
Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038
Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui
2015
Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model. Zbl 1325.33007
Damanik, David; Fillman, Jake; Lukic, Milivoje; Yessen, William
2015
Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian. Zbl 1310.81065
Damanik, David; Gorodetski, Anton
2015
Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians. Zbl 1327.47029
Damanik, David; Gorodetski, Anton
2015
On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168
Damanik, David; Goldstein, Michael
2014
Dynamics of unitary operators. Zbl 1321.47076
Damanik, David; Fillman, Jake; Vance, Robert
2014
Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052
Damanik, David; Fillman, Jake; Gorodetski, Anton
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010
Damanik, David; Munger, Paul; Yessen, William N.
2013
Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. I: The essential support of the measure. Zbl 1283.33005
Damanik, David; Munger, Paul; Yessen, William N.
2013
Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059
Damanik, David; Gorodetski, Anton
2013
Limit-periodic Schrödinger operators on $$\mathbb Z^d$$: uniform localization. Zbl 1285.35005
Damanik, David; Gan, Zheng
2013
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035
Damanik, David; Gorodetski, Anton
2012
Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016
Damanik, David; Gorodetski, Anton
2011
Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023
Damanik, David; Gan, Zheng
2011
Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053
Damanik, David; Gan, Zheng
2011
A continuum version of the Kunz-Souillard approach to localization in one dimension. Zbl 1245.34084
Damanik, David; Stolz, Günter
2011
Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031
Damanik, David; Killip, Rowan; Simon, Barry
2010
A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085
Damanik, David; Tcheremchantsev, Serguei
2010
Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058
Damanik, David; Gan, Zheng
2010
Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312
Damanik, David; Gorodetski, Anton
2009
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009
Damanik, David; Gorodetski, Anton
2009
Schrödinger operators defined by interval-exchange transformations. Zbl 1184.81056
Chaika, Jon; Damanik, David; Krüger, Helge
2009
The repetition property for sequences on tori generated by polynomials or skew-shifts. Zbl 1186.37018
Boshernitzan, Michael; Damanik, David
2009
Almost everything about the Fibonacci operator. Zbl 1175.81090
Damanik, David
2009
Pinned repetitions in symbolic flows: preliminary results. Zbl 1184.37013
Boshernitzan, M.; Damanik, David
2009
Almost periodic Szegő cocycles with uniformly positive Lyapunov exponents. Zbl 1185.37063
Damanik, David; Krüger, Helge
2009
The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097
Damanik, David; Pushnitski, Alexander; Simon, Barry
2008
The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151
Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S.
2008
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian. Zbl 1153.81011
Damanik, David; Tcheremchantsev, Serguei
2008
Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016
Boshernitzan, Michael; Damanik, David
2008
Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations. Zbl 1259.37011
Bjerklöv, Kristian; Damanik, David; Johnson, Russell
2008
Upper bounds in quantum dynamics. Zbl 1114.81036
Damanik, David; Tcheremchantsev, Serguei
2007
Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018
Damanik, David
2007
Strictly ergodic subshifts and associated operators. Zbl 1130.82017
Damanik, David
2007
Schrödinger operators with many bound states. Zbl 1114.34065
Damanik, David; Remling, Christian
2007
Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002
Damanik, David; Lenz, Daniel
2007
Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020
Damanik, David; Naboko, Serguei
2007
Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Zbl 1110.47019
Damanik, David; Teschl, Gerald
2007
A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009
Damanik, David; Lenz, Daniel
2006
Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029
Damanik, David; Simon, Barry
2006
Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030
Damanik, David; Simon, Barry
2006
Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028
Damanik, David; Lenz, Daniel
2006
Lower transport bounds for one-dimensional continuum Schrödinger operators. Zbl 1116.34066
Damanik, David; Lenz, Daniel; Stolz, Günter
2006
Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. Zbl 1132.81018
Damanik, David; Tcheremchantsev, Serguei
2006
Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007
Damanik, David; Lenz, Daniel
2006
Verblunsky coefficients with Coulomb-type decay. Zbl 1100.42016
Damanik, David
2006
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Dynamical upper bounds for one-dimensional quasicrystals. Zbl 1077.81039
Damanik, David
2005
Schrödinger operators with few bound states. Zbl 1082.47029
Damanik, David; Killip, Rowan; Simon, Barry
2005
Ergodic potentials with a discontinuous sampling function are non-deterministic. Zbl 1090.47021
Damanik, David; Killip, Rowan
2005
Almost everywhere positivity of the Lyapunov exponent for the doubling map. Zbl 1087.47037
Damanik, David; Killip, Rowan
2005
Power-law bounds on transfer matrices and quantum dynamics in one dimension. II. Zbl 1059.81055
Damanik, David; Sütő, András; Tcheremchantsev, Serguei
2004
Half-line Schrödinger operators with no bound states. Zbl 1081.47027
Damanik, David; Killip, R. Rowan
2004
Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075
Damanik, David; Killip, Rowan; Simon, Barry
2004
A version of Gordon’s theorem for multi-dimensional Schrödinger operators. Zbl 1062.47038
Damanik, David
2004
Localization for discrete one-dimensional random word models. Zbl 1043.47032
Damanik, David; Sims, Robert; Stolz, Günter
2004
Half-line eigenfunction estimates and purely singular continuous spectrum of zero Lebesgue measure. Zbl 1047.81021
Damanik, David; Lenz, Daniel
2004
Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators. Zbl 1056.34095
Damanik, David; Hundertmark, Dirk
2004
Palindrome complexity. Zbl 1064.68074
Allouche, Jean-Paul; Baake, Michael; Cassaigne, Julien; Damanik, David
2003
Power-law bounds on transfer matrices and quantum dynamics in one dimension. Zbl 1033.81032
Damanik, David; Tcheremchantsev, Serguei
2003
Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027
Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B.
2003
Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032
Damanik, David; Hundertmark, Dirk; Simon, Barry
2003
Powers in Sturmian sequences. Zbl 1030.68068
Damanik, David; Lenz, Daniel
2003
Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Zbl 1081.81521
Damanik, D.; Zamboni, Luca Q.
2003
Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials. Zbl 1173.81315
Damanik, David; Lenz, Daniel
2003
Log-dimensional spectral properties of one-dimensional quasicrystals. Zbl 1075.81024
Damanik, David; Landrigan, Michael
2003
...and 23 more Documents
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#### Cited by 619 Authors

 83 Damanik, David 23 Simon, Barry 22 Fillman, Jake 19 Lenz, Daniel H. 16 de Oliveira, César R. 15 Gorodetskii, Anton Semenovich 15 Pelantová, Edita 15 Stolz, Gunter 13 Avila Cordeiro de Melo, Artur 12 Jitomirskaya, Svetlana Yakovlevna 11 Ong, Darren C. 11 Zamboni, Luca Quardo 10 Krüger, Helge 10 Lukic, Milivoje 10 Yuditskii, Peter Meerovich 9 Liu, Qinghui 9 Marcellán Español, Francisco 8 Chulaevsky, Victor 8 Germinet, François 8 Koelink, Erik 8 Masáková, Zuzana 8 Qu, Yanhui 8 Zinchenko, Maxim 7 Carvalho, Silas L. 7 Christiansen, Jacob Stordal 7 Rampersad, Narad 7 Shallit, Jeffrey O. 7 Tcheremchantsev, Serguei 7 Yessen, William N. 6 Allouche, Jean-Paul Simon 6 Beckus, Siegfried 6 Boumaza, Hakim 6 Choque Rivero, Abdon Eddy 6 García-Ardila, Juan Carlos 6 Garza, Luis E. 6 Glen, Amy 6 Goldstein, Michael 6 Grünbaum, Francisco Alberto 6 Han, Rui 6 Killip, Rowan 6 Klein, Abel 6 Kozhan, Rostyslav V. 6 Marin, Laurent 6 Naboko, Serguei N. 6 Nagel, Jan 6 Remling, Christian 6 Román, Pablo Manuel 6 Rouault, Alain 6 Safronov, Oleg 6 Sims, Robert L. 6 Velázquez, Luis 6 Zhang, Zhenghe 5 Bochi, Jairo 5 Breuer, Jonathan 5 Dette, Holger 5 Frid, Anna Èduardovna 5 Gamboa, Fabrice 5 Gan, Zheng 5 Karpeshina, Yulia E. 5 Last, Yoram 5 Mañas, Manuel 5 Prado, Roberto A. 5 Shterenberg, Roman G. 5 Solomyak, Boris 5 Starosta, Štěpán 5 Zhao, Xin 5 Zhou, Qi 4 Ambrož, Petr 4 Balková, L’ubomíra 4 Cassaigne, Julien 4 Fici, Gabriele 4 Fuentes, Edinson 4 Geronimo, Jeffrey S. 4 Gordon, Alexander Ya. 4 Hamza, Eman 4 Johnson, Russell Allan 4 Joye, Alain 4 Kachkovskiy, Ilya V. 4 Liu, Wencai 4 Munger, Paul E. 4 Najar, Hatem 4 Salo, Ville O. 4 Seifert, Christian 4 Simanek, Brian Z. 4 VandenBoom, Tom 4 Wang, Fengpeng 4 Wen, Zhi-Ying 4 Zhang, Shiwen 3 Anshelevich, Michael 3 Ariznabarreta, Gerardo 3 Baake, Michael 3 Bellissard, Jean V. 3 Bjerklöv, Kristian 3 Boshernitzan, Michael D. 3 Bourgain, Jean 3 Bourget, Olivier 3 Branquinho, Amílcar José Pinto Lopes 3 Brlek, Srečko 3 Bucaj, Valmir 3 Bucci, Michelangelo ...and 519 more Authors
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#### Cited in 155 Serials

 53 Communications in Mathematical Physics 37 Theoretical Computer Science 33 Journal of Functional Analysis 31 Journal of Mathematical Physics 28 Journal of Mathematical Analysis and Applications 26 Annales Henri Poincaré 23 Journal of Approximation Theory 21 Proceedings of the American Mathematical Society 18 Ergodic Theory and Dynamical Systems 16 Journal of Statistical Physics 15 Advances in Mathematics 14 Letters in Mathematical Physics 14 Duke Mathematical Journal 13 Journal of Spectral Theory 12 Constructive Approximation 11 Journal d’Analyse Mathématique 11 Reviews in Mathematical Physics 11 European Journal of Combinatorics 10 Transactions of the American Mathematical Society 9 Mathematical Physics, Analysis and Geometry 8 Integral Equations and Operator Theory 8 Journal of the European Mathematical Society (JEMS) 8 RAIRO. Theoretical Informatics and Applications 7 Inventiones Mathematicae 7 Journal of Differential Equations 7 Advances in Applied Mathematics 6 Discrete Mathematics 6 Journal of Computational and Applied Mathematics 6 Linear Algebra and its Applications 6 Journal of Dynamics and Differential Equations 5 Discrete Applied Mathematics 5 Mathematische Annalen 5 Journal of the American Mathematical Society 5 Discrete and Continuous Dynamical Systems 4 International Journal of Foundations of Computer Science 4 Geometric and Functional Analysis. GAFA 4 Annals of Mathematics. Second Series 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Nonlinearity 3 Mathematische Zeitschrift 3 Probability Theory and Related Fields 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Russian Mathematics 3 Mediterranean Journal of Mathematics 3 Discrete and Continuous Dynamical Systems. Series S 3 Bulletin of Mathematical Sciences 2 Communications on Pure and Applied Mathematics 2 Information Processing Letters 2 Israel Journal of Mathematics 2 Linear and Multilinear Algebra 2 Mathematical Notes 2 Theoretical and Mathematical Physics 2 Arkiv för Matematik 2 Acta Mathematica 2 Annales de l’Institut Fourier 2 Journal of Multivariate Analysis 2 Journal of Statistical Planning and Inference 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Studies in Applied Mathematics 2 Acta Applicandae Mathematicae 2 Physica D 2 SIAM Journal on Matrix Analysis and Applications 2 SIAM Journal on Mathematical Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Journal of Mathematical Sciences (New York) 2 Random Operators and Stochastic Equations 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 The Ramanujan Journal 2 Discrete Mathematics and Theoretical Computer Science. DMTCS 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of High Energy Physics 2 Communications on Pure and Applied Analysis 2 Computational Methods and Function Theory 2 Journal of Discrete Algorithms 2 Oberwolfach Reports 2 Complex Analysis and Operator Theory 2 Frontiers of Mathematics in China 2 Journal of Physics A: Mathematical and Theoretical 2 RAIRO. Theoretical Informatics and Applications 2 Journal of Fractal Geometry 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Studia Mathematica 1 Ukrainian Mathematical Journal 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Acta Arithmetica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Bulletin de la Société Mathématique de France 1 Functional Analysis and its Applications 1 Illinois Journal of Mathematics 1 Journal of Combinatorial Theory. Series A ...and 55 more Serials
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#### Cited in 49 Fields

 265 Operator theory (47-XX) 175 Quantum theory (81-XX) 164 Dynamical systems and ergodic theory (37-XX) 126 Partial differential equations (35-XX) 115 Statistical mechanics, structure of matter (82-XX) 99 Computer science (68-XX) 88 Ordinary differential equations (34-XX) 85 Harmonic analysis on Euclidean spaces (42-XX) 56 Special functions (33-XX) 55 Difference and functional equations (39-XX) 54 Probability theory and stochastic processes (60-XX) 40 Linear and multilinear algebra; matrix theory (15-XX) 35 Number theory (11-XX) 31 Measure and integration (28-XX) 25 Functions of a complex variable (30-XX) 24 Functional analysis (46-XX) 18 Convex and discrete geometry (52-XX) 16 Combinatorics (05-XX) 14 Numerical analysis (65-XX) 9 Global analysis, analysis on manifolds (58-XX) 7 Group theory and generalizations (20-XX) 7 Integral transforms, operational calculus (44-XX) 6 Real functions (26-XX) 6 Approximations and expansions (41-XX) 5 Topological groups, Lie groups (22-XX) 5 Potential theory (31-XX) 4 Statistics (62-XX) 3 General and overarching topics; collections (00-XX) 3 Algebraic geometry (14-XX) 3 Associative rings and algebras (16-XX) 3 Sequences, series, summability (40-XX) 3 General topology (54-XX) 3 Optics, electromagnetic theory (78-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Abstract harmonic analysis (43-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)