Edit Profile (opens in new tab) Damanik, David Compute Distance To: Compute Author ID: damanik.david Published as: Damanik, David; Damanik, D. Documents Indexed: 144 Publications since 1997, including 1 Book 9 Contributions as Editor Co-Authors: 83 Co-Authors with 132 Joint Publications 1,583 Co-Co-Authors all top 5 Co-Authors 20 single-authored 19 Gorodetskii, Anton Semenovich 18 Fillman, Jake 17 Lenz, Daniel H. 11 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 Boshernitzan, Michael D. 4 Sukhtaiev, Selim 3 Fang, Licheng 3 Grimm, Uwe 3 Guo, Shuzheng 3 Hundertmark, Dirk 3 Krüger, Helge 3 Ong, Darren C. 3 Sims, Robert L. 3 VandenBoom, Tom 3 Wang, Fengpeng 3 Yuditskii, Peter Meerovich 3 Zhang, Zhenghe 2 Binder, Ilia A. 2 Bochi, Jairo 2 Bucaj, Valmir 2 del Río Castillo, Rafael René 2 Embree, Mark 2 Gerbuz, Vitaly 2 Gesztesy, Fritz 2 Jitomirskaya, Svetlana Yakovlevna 2 Johnson, Russell Allan 2 Munger, Paul E. 2 Solomyak, Boris 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 Eichinger, Benjamin 1 Erickson, Jon 1 Franco, Asaf L. 1 Gähler, Franz 1 Ghez, Jean-Michel 1 Haynes, Alan K. 1 Helman, Mark 1 Hinkle, Gerhardt 1 Julien, Antoine 1 Jun, Hyunkyu 1 Kellendonk, Johannes 1 Keller, Matthias 1 Kesten, Jacob 1 Landrigan, Michael 1 Last, Yoram 1 Lemm, Marius 1 Liu, Qinghui 1 Martínez-Finkelshtein, Andrei 1 Naboko, Serguei N. 1 Nagnibeda, Tatiana V. 1 Navas, Andrés 1 Pogorzelski, Felix 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 1 Zhou, Zhe all top 5 Serials 16 Communications in Mathematical Physics 14 Journal of Functional Analysis 9 Oberwolfach Reports 8 Annales Henri Poincaré 7 Duke Mathematical Journal 6 Journal of Approximation Theory 6 Journal of Spectral Theory 4 Letters in Mathematical Physics 4 Inventiones Mathematicae 4 Proceedings of the American Mathematical Society 3 Israel Journal of Mathematics 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 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 Journal of Dynamics and Differential Equations 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 Graduate Studies in Mathematics 1 Journal of Modern Dynamics 1 Operators and Matrices 1 Electronic Research Announcements in Mathematical Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Science China. Mathematics 1 Journal of Fractal Geometry 1 Arnold Mathematical Journal all top 5 Fields 89 Operator theory (47-XX) 70 Quantum theory (81-XX) 45 Dynamical systems and ergodic theory (37-XX) 35 Ordinary differential equations (34-XX) 35 Statistical mechanics, structure of matter (82-XX) 30 Partial differential equations (35-XX) 18 Difference and functional equations (39-XX) 9 General and overarching topics; collections (00-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Convex and discrete geometry (52-XX) 7 Number theory (11-XX) 7 Measure and integration (28-XX) 7 Special functions (33-XX) 7 Computer science (68-XX) 5 Combinatorics (05-XX) 4 Probability theory and stochastic processes (60-XX) 2 Global analysis, analysis on manifolds (58-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 Functional analysis (46-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 125 Publications have been cited 1,728 times in 758 Documents Cited by ▼ Year ▼ The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097Damanik, David; Pushnitski, Alexander; Simon, Barry 91 2008 Palindrome complexity. Zbl 1064.68074Allouche, Jean-Paul; Baake, Michael; Cassaigne, Julien; Damanik, David 60 2003 Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity. Zbl 1045.81024Damanik, David; Killip, Rowan; Lenz, Daniel 55 2000 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031Damanik, David; Killip, Rowan; Simon, Barry 53 2010 Schrödinger operators with dynamically defined potentials. Zbl 06823048Damanik, David 42 2017 Localization for one-dimensional, continuum, Bernoulli-Anderson models. Zbl 1107.82025Damanik, David; Sims, Robert; Stolz, Günter 41 2002 Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues. Zbl 0962.81012Damanik, David; Lenz, Daniel 38 1999 Multi-scale analysis implies strong dynamical localization. Zbl 0976.60064Damanik, D.; Stollmann, P. 38 2001 The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S. 35 2008 Gordon-type arguments in the spectral theory of one-dimensional quasicrystals. Zbl 0989.81025Damanik, David 32 2000 The index of Sturmian sequences. Zbl 1002.11020Damanik, David; Lenz, Daniel 32 2002 Power-law bounds on transfer matrices and quantum dynamics in one dimension. Zbl 1033.81032Damanik, David; Tcheremchantsev, Serguei 31 2003 Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016Damanik, David; Gorodetski, Anton 29 2011 Upper bounds in quantum dynamics. Zbl 1114.81036Damanik, David; Tcheremchantsev, Serguei 29 2007 A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009Damanik, David; Lenz, Daniel 28 2006 Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031Damanik, David; Embree, Mark; Gorodetski, Anton 27 2015 Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312Damanik, David; Gorodetski, Anton 24 2009 Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018Damanik, David 23 2007 Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029Damanik, David; Simon, Barry 23 2006 The Fibonacci Hamiltonian. Zbl 1359.81108Damanik, David; Gorodetski, Anton; Yessen, William 23 2016 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012Avila, Artur; Damanik, David 22 2005 Uniform spectral properties of one-dimensional quasicrystals. II: The Lyapunov exponent. Zbl 1044.81036Damanik, David; Lenz, Daniel 22 1999 Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B. 22 2003 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012Avila, Artur; Bochi, Jairo; Damanik, David 22 2009 Half-line Schrödinger operators with no bound states. Zbl 1081.47027Damanik, David; Killip, Rowan 21 2004 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021Avila, Artur; Damanik, David 21 2008 \(\alpha\)-continuity properties of one-dimensional quasicrystals. Zbl 0907.34073Damanik, David 20 1998 Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems. Zbl 1332.82027Damanik, David; Lukic, Milivoje; Yessen, William 20 2015 Local symmetries in the period-doubling sequence. Zbl 0943.68127Damanik, David 19 2000 Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030Damanik, David; Simon, Barry 19 2006 On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168Damanik, David; Goldstein, Michael 18 2014 Power-law bounds on transfer matrices and quantum dynamics in one dimension. II. Zbl 1059.81055Damanik, David; Sütő, András; Tcheremchantsev, Serguei 17 2004 Strictly ergodic subshifts and associated operators. Zbl 1130.82017Damanik, David 17 2007 Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028Damanik, David; Lenz, Daniel 17 2006 Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent. Zbl 1422.35022Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; Vandenboom, Tom; Wang, Fengpeng; Zhang, Zhenghe 17 2019 Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117Damanik, David; Gorodetski, Anton; Solomyak, Boris 16 2015 Dynamics of unitary operators. Zbl 1321.47076Damanik, David; Fillman, Jake; Vance, Robert 16 2014 A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085Damanik, David; Tcheremchantsev, Serguei 16 2010 Powers in Sturmian sequences. Zbl 1030.68068Damanik, David; Lenz, Daniel 15 2003 Lower transport bounds for one-dimensional continuum Schrödinger operators. Zbl 1116.34066Damanik, David; Lenz, Daniel; Stolz, Günter 15 2006 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010Damanik, David; Munger, Paul; Yessen, William N. 15 2013 Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices. Zbl 1332.81066Damanik, David; Fillman, Jake; Ong, Darren C. 14 2016 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. I: The essential support of the measure. Zbl 1283.33005Damanik, David; Munger, Paul; Yessen, William N. 14 2013 Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032Damanik, David; Hundertmark, Dirk; Simon, Barry 14 2003 Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David 14 2016 Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. Zbl 1132.81018Damanik, David; Tcheremchantsev, Serguei 14 2006 On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data. Zbl 1342.35300Damanik, David; Goldstein, Michael 14 2016 Singular continuous spectrum for a class of substitution Hamiltonians. Zbl 0930.11007Damanik, David 13 1998 Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053Damanik, David; Gan, Zheng 13 2011 Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023Damanik, David; Gan, Zheng 13 2011 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007Avila, Artur; Bochi, Jairo; Damanik, David 13 2012 Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian. Zbl 1153.81011Damanik, David; Tcheremchantsev, Serguei 13 2008 Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Zbl 1081.81521Damanik, D.; Zamboni, Luca Q. 12 2003 Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje 12 2018 Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016Boshernitzan, Michael; Damanik, David 12 2008 Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007Damanik, David; Lenz, Daniel 12 2006 The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067Damanik, David; Goldstein, Michael; Lukic, Milivoje 11 2016 Dynamical upper bounds for one-dimensional quasicrystals. Zbl 1077.81039Damanik, David 11 2005 Palindrome complexity bounds for primitive substitution sequences. Zbl 0962.68141Damanik, David; Zare, Douglas 11 2000 Schrödinger operators with few bound states. Zbl 1082.47029Damanik, David; Killip, Rowan; Simon, Barry 11 2005 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089Avila, Artur; Damanik, David; Zhang, Zhenghe 11 2014 The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035Damanik, David; Gorodetski, Anton 11 2012 The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009Damanik, David; Gorodetski, Anton 10 2009 Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058Damanik, David; Gan, Zheng 10 2010 Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113Damanik, David; Fillman, Jake; Lukic, Milivoje 10 2017 Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052Damanik, David; Fillman, Jake; Gorodetski, Anton 10 2014 An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators. Zbl 1344.47021Damanik, David; Gorodetski, Anton 9 2016 Schrödinger operators with many bound states. Zbl 1114.34065Damanik, David; Remling, Christian 9 2007 Substitution Hamiltonians with bounded trace map orbits. Zbl 0996.37011Damanik, David 8 2000 Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure. Zbl 0907.34074Damanik, David 8 1998 Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075Damanik, David; Killip, Rowan; Simon, Barry 8 2004 Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564Damanik, David; Fillman, Jake 8 2019 Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002Damanik, David; Lenz, Daniel 8 2007 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 8 2018 The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095Damanik, David; Goldstein, Michael; Lukic, Milivoje 8 2017 Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020Damanik, David; Naboko, Serguei 7 2007 Ergodic potentials with a discontinuous sampling function are non-deterministic. Zbl 1090.47021Damanik, David; Killip, Rowan 7 2005 Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059Damanik, David; Gorodetski, Anton 7 2013 Uniform singular continuous spectrum for the period doubling Hamiltonian. Zbl 1002.47015Damanik, David 7 2001 Linearly recurrent circle map subshifts and an application to Schrödinger operators. Zbl 1023.47019Adamczewski, B.; Damanik, D. 7 2002 Singular continuous spectrum for a class of substitution Hamiltonians. II. Zbl 1044.81035Damanik, David 7 2000 A version of Gordon’s theorem for multi-dimensional Schrödinger operators. Zbl 1062.47038Damanik, David 7 2004 Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials. Zbl 1173.81315Damanik, David; Lenz, Daniel 7 2003 Linear repetitivity. I: Uniform subadditive ergodic theorems and applications. Zbl 1182.37020Damanik, D.; Lenz, D. 7 2001 A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians. Zbl 1092.81519Damanik, D.; Ghez, J.-M.; Raymond, L. 7 2001 Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037Damanik, David; Yuditskii, Peter 6 2016 On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William 6 2016 Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui 6 2015 Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model. Zbl 1325.33007Damanik, David; Fillman, Jake; Lukic, Milivoje; Yessen, William 6 2015 Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line. Zbl 1342.82120Damanik, David; Erickson, Jon; Fillman, Jake; Hinkle, Gerhardt; Vu, Alan 6 2016 Localization for discrete one-dimensional random word models. Zbl 1043.47032Damanik, David; Sims, Robert; Stolz, Günter 6 2004 Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Zbl 1110.47019Damanik, David; Teschl, Gerald 6 2007 Some high-complexity Hamiltonians with purely singular continuous spectrum. Zbl 1021.34074Damanik, D.; Solomyak, B. 5 2002 A continuum version of the Kunz-Souillard approach to localization in one dimension. Zbl 1245.34084Damanik, David; Stolz, Günter 5 2011 Anderson localization for quasi-periodic CMV matrices and quantum walks. Zbl 1462.35316Wang, Fengpeng; Damanik, David 5 2019 Schrödinger operators defined by interval-exchange transformations. Zbl 1184.81056Chaika, Jon; Damanik, David; Krüger, Helge 5 2009 From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei 5 2016 Limit-periodic Schrödinger operators on \(\mathbb Z^d\): uniform localization. Zbl 1285.35005Damanik, David; Gan, Zheng 4 2013 A generalization of Gordon’s theorem and applications to quasiperiodic Schrödinger operators. Zbl 0954.34074Damanik, David; Stolz, Günter 4 2000 Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations. Zbl 1259.37011Bjerklöv, Kristian; Damanik, David; Johnson, Russell 4 2008 One-dimensional ergodic Schrödinger operators. I. General theory (to appear). Zbl 07517379Damanik, David; Fillman, Jake 1 2022 Localization for Anderson models on metric and discrete tree graphs. Zbl 1436.05027Damanik, David; Fillman, Jake; Sukhtaiev, Selim 3 2020 Zero measure and singular continuous spectra for quantum graphs. Zbl 1442.05124Damanik, David; Fang, Licheng; Sukhtaiev, Selim 2 2020 Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients. Zbl 1466.37021Fang, Licheng; Damanik, David; Guo, Shuzheng 1 2020 Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent. Zbl 1422.35022Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; Vandenboom, Tom; Wang, Fengpeng; Zhang, Zhenghe 17 2019 Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564Damanik, David; Fillman, Jake 8 2019 Anderson localization for quasi-periodic CMV matrices and quantum walks. Zbl 1462.35316Wang, Fengpeng; Damanik, David 5 2019 Multidimensional almost-periodic Schrödinger operators with Cantor spectrum. Zbl 1474.34608Damanik, David; Fillman, Jake; Gorodetski, Anton 4 2019 Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly. Zbl 1478.35108Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; VandenBoom, Tom; Wang, Fengpeng; Zhang, Zhenghe 3 2019 Anderson localization for radial tree graphs with random branching numbers. Zbl 1481.05140Damanik, David; Sukhtaiev, Selim 2 2019 Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje 12 2018 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 8 2018 Almost periodicity in time of solutions of the Toda lattice. Zbl 1396.37067Binder, Ilia; Damanik, David; Lukic, Milivoje; VandenBoom, Tom 4 2018 Spectral transitions for the square Fibonacci Hamiltonian. Zbl 06979900Damanik, David; Gorodetski, Anton 2 2018 Schrödinger operators with dynamically defined potentials. Zbl 06823048Damanik, David 42 2017 Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113Damanik, David; Fillman, Jake; Lukic, Milivoje 10 2017 The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095Damanik, David; Goldstein, Michael; Lukic, Milivoje 8 2017 A multi-scale analysis scheme on abelian groups with an application to operators dual to Hill’s equation. Zbl 1355.35053Damanik, David; Goldstein, Michael; Lukic, Milivoje 4 2017 The Fibonacci Hamiltonian. Zbl 1359.81108Damanik, David; Gorodetski, Anton; Yessen, William 23 2016 Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices. Zbl 1332.81066Damanik, David; Fillman, Jake; Ong, Darren C. 14 2016 Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David 14 2016 On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data. Zbl 1342.35300Damanik, David; Goldstein, Michael 14 2016 The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067Damanik, David; Goldstein, Michael; Lukic, Milivoje 11 2016 An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators. Zbl 1344.47021Damanik, David; Gorodetski, Anton 9 2016 Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037Damanik, David; Yuditskii, Peter 6 2016 On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William 6 2016 Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line. Zbl 1342.82120Damanik, David; Erickson, Jon; Fillman, Jake; Hinkle, Gerhardt; Vu, Alan 6 2016 From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei 5 2016 What is \(\ldots \) aperiodic order? Zbl 1352.52028Baake, Michael; Damanik, David; Grimm, Uwe 4 2016 Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031Damanik, David; Embree, Mark; Gorodetski, Anton 27 2015 Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems. Zbl 1332.82027Damanik, David; Lukic, Milivoje; Yessen, William 20 2015 Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117Damanik, David; Gorodetski, Anton; Solomyak, Boris 16 2015 Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui 6 2015 Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model. Zbl 1325.33007Damanik, David; Fillman, Jake; Lukic, Milivoje; Yessen, William 6 2015 Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian. Zbl 1310.81065Damanik, David; Gorodetski, Anton 3 2015 Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians. Zbl 1327.47029Damanik, David; Gorodetski, Anton 2 2015 On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168Damanik, David; Goldstein, Michael 18 2014 Dynamics of unitary operators. Zbl 1321.47076Damanik, David; Fillman, Jake; Vance, Robert 16 2014 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089Avila, Artur; Damanik, David; Zhang, Zhenghe 11 2014 Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052Damanik, David; Fillman, Jake; Gorodetski, Anton 10 2014 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010Damanik, David; Munger, Paul; Yessen, William N. 15 2013 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. I: The essential support of the measure. Zbl 1283.33005Damanik, David; Munger, Paul; Yessen, William N. 14 2013 Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059Damanik, David; Gorodetski, Anton 7 2013 Limit-periodic Schrödinger operators on \(\mathbb Z^d\): uniform localization. Zbl 1285.35005Damanik, David; Gan, Zheng 4 2013 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007Avila, Artur; Bochi, Jairo; Damanik, David 13 2012 The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035Damanik, David; Gorodetski, Anton 11 2012 Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016Damanik, David; Gorodetski, Anton 29 2011 Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053Damanik, David; Gan, Zheng 13 2011 Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023Damanik, David; Gan, Zheng 13 2011 A continuum version of the Kunz-Souillard approach to localization in one dimension. Zbl 1245.34084Damanik, David; Stolz, Günter 5 2011 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031Damanik, David; Killip, Rowan; Simon, Barry 53 2010 A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085Damanik, David; Tcheremchantsev, Serguei 16 2010 Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058Damanik, David; Gan, Zheng 10 2010 Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312Damanik, David; Gorodetski, Anton 24 2009 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012Avila, Artur; Bochi, Jairo; Damanik, David 22 2009 The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009Damanik, David; Gorodetski, Anton 10 2009 Schrödinger operators defined by interval-exchange transformations. Zbl 1184.81056Chaika, Jon; Damanik, David; Krüger, Helge 5 2009 The repetition property for sequences on tori generated by polynomials or skew-shifts. Zbl 1186.37018Boshernitzan, Michael; Damanik, David 4 2009 Almost everything about the Fibonacci operator. Zbl 1175.81090Damanik, David 2 2009 Pinned repetitions in symbolic flows: preliminary results. Zbl 1184.37013Boshernitzan, M.; Damanik, David 2 2009 Almost periodic Szegő cocycles with uniformly positive Lyapunov exponents. Zbl 1185.37063Damanik, David; Krüger, Helge 1 2009 The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097Damanik, David; Pushnitski, Alexander; Simon, Barry 91 2008 The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S. 35 2008 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021Avila, Artur; Damanik, David 21 2008 Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian. Zbl 1153.81011Damanik, David; Tcheremchantsev, Serguei 13 2008 Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016Boshernitzan, Michael; Damanik, David 12 2008 Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations. Zbl 1259.37011Bjerklöv, Kristian; Damanik, David; Johnson, Russell 4 2008 Upper bounds in quantum dynamics. Zbl 1114.81036Damanik, David; Tcheremchantsev, Serguei 29 2007 Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018Damanik, David 23 2007 Strictly ergodic subshifts and associated operators. Zbl 1130.82017Damanik, David 17 2007 Schrödinger operators with many bound states. Zbl 1114.34065Damanik, David; Remling, Christian 9 2007 Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002Damanik, David; Lenz, Daniel 8 2007 Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020Damanik, David; Naboko, Serguei 7 2007 Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Zbl 1110.47019Damanik, David; Teschl, Gerald 6 2007 A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009Damanik, David; Lenz, Daniel 28 2006 Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029Damanik, David; Simon, Barry 23 2006 Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030Damanik, David; Simon, Barry 19 2006 Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028Damanik, David; Lenz, Daniel 17 2006 Lower transport bounds for one-dimensional continuum Schrödinger operators. Zbl 1116.34066Damanik, David; Lenz, Daniel; Stolz, Günter 15 2006 Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. Zbl 1132.81018Damanik, David; Tcheremchantsev, Serguei 14 2006 Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007Damanik, David; Lenz, Daniel 12 2006 Verblunsky coefficients with Coulomb-type decay. Zbl 1100.42016Damanik, David 2 2006 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012Avila, Artur; Damanik, David 22 2005 Dynamical upper bounds for one-dimensional quasicrystals. Zbl 1077.81039Damanik, David 11 2005 Schrödinger operators with few bound states. Zbl 1082.47029Damanik, David; Killip, Rowan; Simon, Barry 11 2005 Ergodic potentials with a discontinuous sampling function are non-deterministic. Zbl 1090.47021Damanik, David; Killip, Rowan 7 2005 Almost everywhere positivity of the Lyapunov exponent for the doubling map. Zbl 1087.47037Damanik, David; Killip, Rowan 2 2005 Half-line Schrödinger operators with no bound states. Zbl 1081.47027Damanik, David; Killip, Rowan 21 2004 Power-law bounds on transfer matrices and quantum dynamics in one dimension. II. Zbl 1059.81055Damanik, David; Sütő, András; Tcheremchantsev, Serguei 17 2004 Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075Damanik, David; Killip, Rowan; Simon, Barry 8 2004 A version of Gordon’s theorem for multi-dimensional Schrödinger operators. Zbl 1062.47038Damanik, David 7 2004 Localization for discrete one-dimensional random word models. Zbl 1043.47032Damanik, David; Sims, Robert; Stolz, Günter 6 2004 Half-line eigenfunction estimates and purely singular continuous spectrum of zero Lebesgue measure. Zbl 1047.81021Damanik, David; Lenz, Daniel 3 2004 Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators. Zbl 1056.34095Damanik, David; Hundertmark, Dirk 1 2004 Palindrome complexity. Zbl 1064.68074Allouche, Jean-Paul; Baake, Michael; Cassaigne, Julien; Damanik, David 60 2003 Power-law bounds on transfer matrices and quantum dynamics in one dimension. Zbl 1033.81032Damanik, David; Tcheremchantsev, Serguei 31 2003 Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B. 22 2003 Powers in Sturmian sequences. Zbl 1030.68068Damanik, David; Lenz, Daniel 15 2003 Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032Damanik, David; Hundertmark, Dirk; Simon, Barry 14 2003 Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Zbl 1081.81521Damanik, D.; Zamboni, Luca Q. 12 2003 ...and 25 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 661 Authors 90 Damanik, David 25 Fillman, Jake 23 Simon, Barry 20 Lenz, Daniel H. 17 de Oliveira, César R. 17 Pelantová, Edita 16 Gorodetskii, Anton Semenovich 15 Stolz, Gunter 13 Avila Cordeiro de Melo, Artur 13 Jitomirskaya, Svetlana Yakovlevna 13 Ong, Darren C. 11 Lukic, Milivoje 11 Zamboni, Luca Quardo 10 Krüger, Helge 10 Yuditskii, Peter Meerovich 9 Liu, Qinghui 9 Marcellán Español, Francisco 8 Carvalho, Silas L. 8 Chulaevsky, Victor 8 Germinet, François 8 Koelink, Erik 8 Masáková, Zuzana 8 Qu, Yanhui 8 Rampersad, Narad 8 Shallit, Jeffrey O. 8 Zinchenko, Maxim 7 Christiansen, Jacob Stordal 7 Garza, Luis E. 7 Grünbaum, Francisco Alberto 7 Naboko, Serguei N. 7 Nagel, Jan 7 Rouault, Alain 7 Safronov, Oleg 7 Tcheremchantsev, Serguei 7 Velázquez, Luis 7 Yessen, William N. 6 Allouche, Jean-Paul Simon 6 Beckus, Siegfried 6 Boumaza, Hakim 6 Choque Rivero, Abdon Eddy 6 Frid, Anna Èduardovna 6 Gamboa, Fabrice 6 García-Ardila, Juan Carlos 6 Glen, Amy 6 Goldstein, Michael 6 Han, Rui 6 Killip, Rowan 6 Klein, Abel 6 Kozhan, Rostyslav V. 6 Marin, Laurent 6 Remling, Christian 6 Román, Pablo Manuel 6 Salo, Ville O. 6 Sims, Robert L. 6 Zhang, Zhenghe 6 Zhao, Xin 5 Bochi, Jairo 5 Breuer, Jonathan 5 Cassaigne, Julien 5 Dette, Holger 5 Eichinger, Benjamin 5 Fuentes, Edinson 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 Werner, Albert H. 5 Zhang, Shiwen 5 Zhou, Qi 4 Ambrož, Petr 4 Balková, L’ubomíra 4 Boshernitzan, Michael D. 4 Cedzich, Christopher 4 Ekanga, Trésor 4 Fici, Gabriele 4 Geronimo, Jeffrey S. 4 Golinskii, Leonid Borisovich 4 Gordon, Alexander Ya. 4 Guo, Shuzheng 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 Sakhnovich, Alexander L. 4 Seifert, Christian 4 Simanek, Brian Z. 4 Świderski, Grzegorz 4 Takahashi, Yuki 4 VandenBoom, Tom 4 Wang, Fengpeng 4 Wen, Zhi-Ying 4 You, Jiangong 3 Aloisio, Moacir ...and 561 more Authors all top 5 Cited in 167 Serials 58 Communications in Mathematical Physics 38 Theoretical Computer Science 33 Journal of Functional Analysis 32 Journal of Mathematical Physics 29 Journal of Mathematical Analysis and Applications 27 Annales Henri Poincaré 24 Journal of Approximation Theory 22 Proceedings of the American Mathematical Society 19 Ergodic Theory and Dynamical Systems 16 Journal of Statistical Physics 15 Letters in Mathematical Physics 15 Advances in Mathematics 15 Duke Mathematical Journal 14 Journal of Spectral Theory 13 Reviews in Mathematical Physics 13 Constructive Approximation 11 Journal d’Analyse Mathématique 11 Transactions of the American Mathematical Society 11 European Journal of Combinatorics 9 Mathematical Physics, Analysis and Geometry 9 Journal of the European Mathematical Society (JEMS) 8 Integral Equations and Operator Theory 8 Journal of Dynamics and Differential Equations 8 RAIRO. 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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 Regular and Chaotic Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of High Energy Physics 2 Dynamical Systems 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Communications on Pure and Applied Analysis 2 Computational Methods and Function Theory 2 Journal of Discrete Algorithms 2 Oberwolfach Reports 2 Frontiers of Mathematics in China 2 Journal of Physics A: Mathematical and Theoretical 2 Operators and Matrices 2 Probability Surveys 2 Random Matrices: Theory and Applications 2 Analysis and Mathematical Physics 2 Journal of Fractal Geometry 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 International Journal of Theoretical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Studia Mathematica ...and 67 more Serials all top 5 Cited in 49 Fields 291 Operator theory (47-XX) 184 Quantum theory (81-XX) 180 Dynamical systems and ergodic theory (37-XX) 136 Partial differential equations (35-XX) 126 Statistical mechanics, structure of matter (82-XX) 112 Computer science (68-XX) 96 Ordinary differential equations (34-XX) 90 Harmonic analysis on Euclidean spaces (42-XX) 60 Special functions (33-XX) 60 Difference and functional equations (39-XX) 59 Probability theory and stochastic processes (60-XX) 43 Linear and multilinear algebra; matrix theory (15-XX) 39 Number theory (11-XX) 33 Measure and integration (28-XX) 27 Functions of a complex variable (30-XX) 24 Functional analysis (46-XX) 19 Convex and discrete geometry (52-XX) 18 Combinatorics (05-XX) 14 Numerical analysis (65-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Group theory and generalizations (20-XX) 7 Approximations and expansions (41-XX) 7 Integral transforms, operational calculus (44-XX) 6 Real functions (26-XX) 5 Topological groups, Lie groups (22-XX) 5 Potential theory (31-XX) 5 Statistics (62-XX) 4 Optics, electromagnetic theory (78-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) 2 Mathematical logic and foundations (03-XX) 2 Abstract harmonic analysis (43-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 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 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) Citations by Year