Edit Profile (opens in new tab) Damanik, David Co-Author Distance Author ID: damanik.david Published as: Damanik, David; Damanik, D. Videos: carmin.tv Documents Indexed: 181 Publications since 1997, including 1 Book and 21 Additional arXiv Preprints 10 Contributions as Editor Co-Authors: 100 Co-Authors with 167 Joint Publications 2,081 Co-Co-Authors all top 5 Co-Authors 23 single-authored 28 Fillman, Jake 22 Gorodetskii, Anton Semenovich 18 Lenz, Daniel H. 13 Lukic, Milivoje 9 Avila, Artur 9 Killip, Rowan 8 Goldstein, Michael 8 Simon, Barry 8 Yessen, William N. 7 Tcheremchantsev, Serguei 6 Stolz, Gunter 6 Zhang, Zhenghe 5 Baake, Michael 5 Gan, Zheng 4 Boshernitzan, Michael D. 4 Embree, Mark 4 Guo, Shuzheng 4 Ong, Darren C. 4 Sukhtaiev, Selim 4 Xu, Fei 4 Yuditskii, Peter Meerovich 3 Fang, Licheng 3 Grimm, Uwe 3 Hundertmark, Dirk 3 Krüger, Helge 3 Sims, Robert L. 3 VandenBoom, Tom 3 Wang, Fengpeng 3 Zhou, Qi 3 Zhou, Zhe 2 Binder, Ilia A. 2 Bochi, Jairo 2 Bucaj, Valmir 2 Chaika, Jonathan 2 del Río Castillo, Rafael René 2 Gerbuz, Vitaly 2 Gesztesy, Fritz 2 Gohlke, Philipp 2 Jitomirskaya, Svetlana Yakovlevna 2 Johnson, Russell Allan 2 Lemm, Marius 2 Liu, Qinghui 2 Malinovitch, Tal 2 Munger, Paul E. 2 Naboko, Serguei N. 2 Qu, Yanhui 2 Solomyak, Boris 2 Young, Giorgio 2 Zamboni, Luca Quardo 2 Zhang, Meirong 1 Adamczewski, Boris 1 Adiceam, Faustin 1 Allouche, Jean-Paul Simon 1 Avron, Joseph E. 1 Berthé, Valérie 1 Bjerklöv, Kristian 1 Black, Adam 1 Breuer, Jonathan 1 Cassaigne, Julien 1 Cortez, Maria Isabel 1 Eichinger, Benjamin 1 Emilsdottir, Iris 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 Li, Xianzhe 1 Martínez-Finkelshtein, Andrei 1 Mei, May 1 Meng, Gang 1 Navas, Andrés 1 Pogorzelski, Felix 1 Pushnitski, Alexander B. 1 Raymond, Laurent 1 Remling, Christian 1 Sadun, Lorenzo A. 1 Schlag, Wilhelm 1 Smirnova-Nagnibeda, Tatiana 1 Stollmann, Peter 1 Strungaru, Nicolae 1 Sütő, András 1 Teschl, Gerald 1 Vance, Robert 1 Voda, Mircea 1 Volberg, Alexander Lvovich 1 Vu, Alan 1 Wang, Chunyi 1 Weiss, Barak 1 You, Jiangong 1 Zare, Douglas all top 5 Serials 18 Communications in Mathematical Physics 16 Journal of Functional Analysis 10 Oberwolfach Reports 10 Journal of Spectral Theory 9 Annales Henri Poincaré 7 Duke Mathematical Journal 6 Journal of Approximation Theory 5 Inventiones Mathematicae 4 Letters in Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 3 Israel Journal of Mathematics 3 Journal d’Analyse Mathématique 3 Journal of Mathematical Analysis and Applications 3 Mathematische Annalen 3 IMRN. International Mathematics Research Notices 3 Geometric and Functional Analysis. GAFA 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Advances in Mathematics 2 European Journal of Combinatorics 2 Journal of the American Mathematical Society 2 Forum Mathematicum 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 Mathematische Nachrichten 1 Mathematische Zeitschrift 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 99 Operator theory (47-XX) 76 Quantum theory (81-XX) 56 Dynamical systems and ergodic theory (37-XX) 39 Partial differential equations (35-XX) 38 Ordinary differential equations (34-XX) 35 Statistical mechanics, structure of matter (82-XX) 19 Difference and functional equations (39-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 10 General and overarching topics; collections (00-XX) 10 Convex and discrete geometry (52-XX) 9 Computer science (68-XX) 8 Number theory (11-XX) 8 Special functions (33-XX) 7 Measure and integration (28-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Combinatorics (05-XX) 4 Abstract harmonic analysis (43-XX) 4 Probability theory and stochastic processes (60-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 Functional analysis (46-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 146 Publications have been cited 2,221 times in 978 Documents Cited by ▼ Year ▼ The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097 Damanik, David; Pushnitski, Alexander; Simon, Barry 116 2008 Schrödinger operators with dynamically defined potentials. Zbl 1541.81060 Damanik, David 75 2017 Palindrome complexity. Zbl 1064.68074 Allouche, Jean-Paul; Baake, Michael; Cassaigne, Julien; Damanik, David 71 2003 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031 Damanik, David; Killip, Rowan; Simon, Barry 60 2010 Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity. Zbl 1045.81024 Damanik, David; Killip, Rowan; Lenz, Daniel 58 2000 Localization for one-dimensional, continuum, Bernoulli-Anderson models. Zbl 1107.82025 Damanik, David; Sims, Robert; Stolz, Günter 50 2002 Multi-scale analysis implies strong dynamical localization. Zbl 0976.60064 Damanik, D.; Stollmann, P. 44 2001 Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues. Zbl 0962.81012 Damanik, David; Lenz, Daniel 42 1999 Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031 Damanik, David; Embree, Mark; Gorodetski, Anton 41 2015 The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151 Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S. 39 2008 Gordon-type arguments in the spectral theory of one-dimensional quasicrystals. Zbl 0989.81025 Damanik, David 38 2000 The index of Sturmian sequences. Zbl 1002.11020 Damanik, David; Lenz, Daniel 37 2002 A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009 Damanik, David; Lenz, Daniel 35 2006 Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016 Damanik, David; Gorodetski, Anton 34 2011 Power-law bounds on transfer matrices and quantum dynamics in one dimension. Zbl 1033.81032 Damanik, David; Tcheremchantsev, Serguei 33 2003 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 32 2019 Upper bounds in quantum dynamics. Zbl 1114.81036 Damanik, David; Tcheremchantsev, Serguei 32 2007 The Fibonacci Hamiltonian. Zbl 1359.81108 Damanik, David; Gorodetski, Anton; Yessen, William 32 2016 Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018 Damanik, David 30 2007 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021 Avila, Artur; Damanik, David 30 2008 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012 Avila, Artur; Bochi, Jairo; Damanik, David 29 2009 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 29 2015 Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027 Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B. 27 2003 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012 Avila, Artur; Damanik, David 27 2005 Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029 Damanik, David; Simon, Barry 27 2006 Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325 Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje 25 2018 Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312 Damanik, David; Gorodetski, Anton 25 2009 Local symmetries in the period-doubling sequence. Zbl 0943.68127 Damanik, David 23 2000 Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077 Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David 23 2016 On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168 Damanik, David; Goldstein, Michael 23 2014 Strictly ergodic subshifts and associated operators. Zbl 1130.82017 Damanik, David 23 2007 Half-line Schrödinger operators with no bound states. Zbl 1081.47027 Damanik, David; Killip, Rowan 23 2004 Uniform spectral properties of one-dimensional quasicrystals. II: The Lyapunov exponent. Zbl 1044.81036 Damanik, David; Lenz, Daniel 22 1999 Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030 Damanik, David; Simon, Barry 22 2006 On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data. Zbl 1342.35300 Damanik, David; Goldstein, Michael 22 2016 \(\alpha\)-continuity properties of one-dimensional quasicrystals. Zbl 0907.34073 Damanik, David 20 1998 Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007 Damanik, David; Lenz, Daniel 20 2006 Dynamics of unitary operators. Zbl 1321.47076 Damanik, David; Fillman, Jake; Vance, Robert 20 2014 Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117 Damanik, David; Gorodetski, Anton; Solomyak, Boris 20 2015 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. 19 2016 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007 Avila, Artur; Bochi, Jairo; Damanik, David 19 2012 Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028 Damanik, David; Lenz, Daniel 19 2006 A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085 Damanik, David; Tcheremchantsev, Serguei 18 2010 Powers in Sturmian sequences. Zbl 1030.68068 Damanik, David; Lenz, Daniel 17 2003 Power-law bounds on transfer matrices and quantum dynamics in one dimension. II. Zbl 1059.81055 Damanik, David; Sütő, András; Tcheremchantsev, Serguei 17 2004 Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023 Damanik, David; Gan, Zheng 17 2011 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023 Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 17 2018 Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032 Damanik, David; Hundertmark, Dirk; Simon, Barry 16 2003 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010 Damanik, David; Munger, Paul; Yessen, William N. 16 2013 Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053 Damanik, David; Gan, Zheng 16 2011 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089 Avila, Artur; Damanik, David; Zhang, Zhenghe 15 2014 Lower transport bounds for one-dimensional continuum Schrödinger operators. Zbl 1116.34066 Damanik, David; Lenz, Daniel; Stolz, Günter 15 2006 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 15 2008 One-dimensional ergodic Schrödinger operators. I. General theory. Zbl 1504.58001 Damanik, David; Fillman, Jake 15 2022 Singular continuous spectrum for a class of substitution Hamiltonians. Zbl 0930.11007 Damanik, David 14 1998 Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016 Boshernitzan, Michael; Damanik, David 14 2008 Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052 Damanik, David; Fillman, Jake; Gorodetski, Anton 14 2014 Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. Zbl 1132.81018 Damanik, David; Tcheremchantsev, Serguei 14 2006 The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067 Damanik, David; Goldstein, Michael; Lukic, Milivoje 14 2016 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. 14 2013 Palindrome complexity bounds for primitive substitution sequences. Zbl 0962.68141 Damanik, David; Zare, Douglas 13 2000 Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Zbl 1081.81521 Damanik, D.; Zamboni, Luca Q. 13 2003 Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058 Damanik, David; Gan, Zheng 13 2010 Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564 Damanik, David; Fillman, Jake 13 2019 Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113 Damanik, David; Fillman, Jake; Lukic, Milivoje 13 2017 Schrödinger operators with few bound states. Zbl 1082.47029 Damanik, David; Killip, Rowan; Simon, Barry 12 2005 The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035 Damanik, David; Gorodetski, Anton 12 2012 Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020 Damanik, David; Naboko, Serguei 12 2007 Dynamical upper bounds for one-dimensional quasicrystals. Zbl 1077.81039 Damanik, David 11 2005 Anderson localization for quasi-periodic CMV matrices and quantum walks. Zbl 1462.35316 Wang, Fengpeng; Damanik, David 11 2019 The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009 Damanik, David; Gorodetski, Anton 11 2009 Schrödinger operators with many bound states. Zbl 1114.34065 Damanik, David; Remling, Christian 11 2007 Substitution Hamiltonians with bounded trace map orbits. Zbl 0996.37011 Damanik, David 10 2000 The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095 Damanik, David; Goldstein, Michael; Lukic, Milivoje 10 2017 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 10 2016 Linear repetitivity. I: Uniform subadditive ergodic theorems and applications. Zbl 1182.37020 Damanik, D.; Lenz, D. 9 2001 Uniform singular continuous spectrum for the period doubling Hamiltonian. Zbl 1002.47015 Damanik, David 9 2001 Almost everywhere positivity of the Lyapunov exponent for the doubling map. Zbl 1087.47037 Damanik, David; Killip, Rowan 9 2005 Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials. Zbl 1173.81315 Damanik, David; Lenz, Daniel 9 2003 A version of Gordon’s theorem for multi-dimensional Schrödinger operators. Zbl 1062.47038 Damanik, David 8 2004 Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075 Damanik, David; Killip, Rowan; Simon, Barry 8 2004 Localization for discrete one-dimensional random word models. Zbl 1043.47032 Damanik, David; Sims, Robert; Stolz, Günter 8 2004 Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059 Damanik, David; Gorodetski, Anton 8 2013 Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure. Zbl 0907.34074 Damanik, David 8 1998 Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002 Damanik, David; Lenz, Daniel 8 2007 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 8 2015 Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037 Damanik, David; Yuditskii, Peter 8 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 8 2016 Linearly recurrent circle map subshifts and an application to Schrödinger operators. Zbl 1023.47019 Adamczewski, B.; Damanik, D. 7 2002 A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians. Zbl 1092.81519 Damanik, D.; Ghez, J.-M.; Raymond, L. 7 2001 Singular continuous spectrum for a class of substitution Hamiltonians. II. Zbl 1044.81035 Damanik, David 7 2000 Ergodic potentials with a discontinuous sampling function are non-deterministic. Zbl 1090.47021 Damanik, David; Killip, Rowan 7 2005 A generalization of Gordon’s theorem and applications to quasiperiodic Schrödinger operators. Zbl 0954.34074 Damanik, David; Stolz, Günter 7 2000 On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009 Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William 7 2016 Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038 Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui 7 2015 Limit-periodic Schrödinger operators on \(\mathbb Z^d\): uniform localization. Zbl 1285.35005 Damanik, David; Gan, Zheng 7 2013 Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Zbl 1110.47019 Damanik, David; Teschl, Gerald 7 2007 From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037 Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei 7 2016 Half-line eigenfunction estimates and purely singular continuous spectrum of zero Lebesgue measure. Zbl 1047.81021 Damanik, David; Lenz, Daniel 6 2004 Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly. Zbl 1478.35108 Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; VandenBoom, Tom; Wang, Fengpeng; Zhang, Zhenghe 6 2019 The rotation number for almost periodic potentials with jump discontinuities and \(\delta \)-interactions. Zbl 1537.34090 Damanik, David; Zhang, Meirong; Zhou, Zhe 1 2024 Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent. Zbl 1511.37038 Avila, Artur; Damanik, David; Zhang, Zhenghe 6 2023 The almost sure essential spectrum of the doubling map model is connected. Zbl 07687744 Damanik, David; Fillman, Jake 3 2023 The spectrum of Schrödinger operators with randomly perturbed ergodic potentials. Zbl 07680038 Avila, Artur; Damanik, David; Gorodetski, Anton 3 2023 Stability of spectral types of quasi-periodic Schrödinger operators with respect to perturbations by decaying potentials. Zbl 1537.81103 Damanik, David; Li, Xianzhe; You, Jiangong; Zhou, Qi 2 2023 Thin spectra and singular continuous spectral measures for limit-periodic Jacobi matrices. Zbl 07750714 Damanik, David; Fillman, Jake; Wang, Chunyi 1 2023 Johnson-Schwartzman gap labelling for ergodic Jacobi matrices. Zbl 07761486 Damanik, David; Fillman, Jake; Zhang, Zhenghe 1 2023 One-dimensional ergodic Schrödinger operators. I. General theory. Zbl 1504.58001 Damanik, David; Fillman, Jake 15 2022 Must the spectrum of a random Schrödinger operator contain an interval? Zbl 07565222 Damanik, David; Gorodetski, Anton 6 2022 Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients. Zbl 07578588 Li, Long; Damanik, David; Zhou, Qi 4 2022 Subordinacy theory for extended CMV matrices. Zbl 1503.47042 Guo, Shuzheng; Damanik, David; Ong, Darren C. 3 2022 Zero measure spectrum for multi-frequency Schrödinger operators. Zbl 1518.47054 Chaika, Jon; Damanik, David; Fillman, Jake; Gohlke, Philipp 3 2022 Spectral characteristics of Schrödinger operators generated by product systems. Zbl 1528.35037 Damanik, David; Fillman, Jake; Gohlke, Philipp 2 2022 The rotation number for almost periodic Schrödinger operators with \(\delta \)-potentials. Zbl 1493.34232 Damanik, David; Zhou, Zhe 2 2022 Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients. Zbl 07605366 Li, Long; Damanik, David; Zhou, Qi 2 2022 Simon’s OPUC Hausdorff dimension conjecture. Zbl 1496.42035 Damanik, David; Guo, Shuzheng; Ong, Darren C. 1 2022 Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set. Zbl 1460.81026 Damanik, David; Fillman, Jake; Gorodetski, Anton 3 2021 Random Hamiltonians with arbitrary point interactions in one dimension. Zbl 1521.47071 Damanik, David; Fillman, Jake; Helman, Mark; Kesten, Jacob; Sukhtaiev, Selim 2 2021 Szegő’s theorem for canonical systems: the Arov gauge and a sum rule. Zbl 1507.42022 Damanik, David; Eichinger, Benjamin; Yuditskii, Peter 1 2021 Zero measure and singular continuous spectra for quantum graphs. Zbl 1442.05124 Damanik, David; Fang, Licheng; Sukhtaiev, Selim 6 2020 Localization for Anderson models on metric and discrete tree graphs. Zbl 1436.05027 Damanik, David; Fillman, Jake; Sukhtaiev, Selim 5 2020 Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients. Zbl 1466.37021 Fang, Licheng; Damanik, David; Guo, Shuzheng 5 2020 Spectral properties of limit-periodic operators. Zbl 1515.47047 Damanik, David; Fillman, Jake 4 2020 Random Sturm-Liouville operators with generalized point interactions. Zbl 1488.34486 Damanik, David; Del Rio, Rafael; Franco, Asaf L. 1 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 32 2019 Limit-periodic Schrödinger operators with Lipschitz continuous IDS. Zbl 07020564 Damanik, David; Fillman, Jake 13 2019 Anderson localization for quasi-periodic CMV matrices and quantum walks. Zbl 1462.35316 Wang, Fengpeng; Damanik, David 11 2019 Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly. Zbl 1478.35108 Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; VandenBoom, Tom; Wang, Fengpeng; Zhang, Zhenghe 6 2019 Multidimensional almost-periodic Schrödinger operators with Cantor spectrum. Zbl 1474.34608 Damanik, David; Fillman, Jake; Gorodetski, Anton 6 2019 Anderson localization for radial tree graphs with random branching numbers. Zbl 1481.05140 Damanik, David; Sukhtaiev, Selim 3 2019 Almost periodicity in time of solutions of the KdV equation. Zbl 1406.35325 Binder, Ilia; Damanik, David; Goldstein, Michael; Lukic, Milivoje 25 2018 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023 Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 17 2018 Almost periodicity in time of solutions of the Toda lattice. Zbl 1396.37067 Binder, Ilia; Damanik, David; Lukic, Milivoje; VandenBoom, Tom 4 2018 Spectral transitions for the square Fibonacci Hamiltonian. Zbl 1503.47059 Damanik, David; Gorodetski, Anton 2 2018 Schrödinger operators with dynamically defined potentials. Zbl 1541.81060 Damanik, David 75 2017 Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum. Zbl 1432.34113 Damanik, David; Fillman, Jake; Lukic, Milivoje 13 2017 The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations. Zbl 1359.34095 Damanik, David; Goldstein, Michael; Lukic, Milivoje 10 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 4 2017 The Fibonacci Hamiltonian. Zbl 1359.81108 Damanik, David; Gorodetski, Anton; Yessen, William 32 2016 Characterizations of uniform hyperbolicity and spectra of CMV matrices. Zbl 1366.37077 Yessen, William; Lukic, Milivoje; Fillman, Jake; Damanik, David 23 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 22 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. 19 2016 The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. Zbl 1350.34067 Damanik, David; Goldstein, Michael; Lukic, Milivoje 14 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 10 2016 Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces. Zbl 1337.37037 Damanik, David; Yuditskii, Peter 8 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 8 2016 On anomalous Lieb-Robinson bounds for the Fibonacci XY chain. Zbl 1350.81009 Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William 7 2016 From mathematical physics to analysis: a walk in Barry Simon’s mathematical garden. II. Zbl 1352.01037 Avron, Joseph; Jitomirskaya, Svetlana; Damanik, David; Breuer, Jonathan; Last, Yoram; Martínez-Finkelshtein, Andrei 7 2016 What is \(\ldots \) aperiodic order? Zbl 1352.52028 Baake, Michael; Damanik, David; Grimm, Uwe 5 2016 Open problems and conjectures related to the theory of mathematical quasicrystals. Zbl 1349.52020 Adiceam, Faustin; Damanik, David; Gähler, Franz; Grimm, Uwe; Haynes, Alan; Julien, Antoine; Navas, Andrés; Sadun, Lorenzo; Weiss, Barak 3 2016 Spectral properties of Schrödinger operators arising in the study of quasicrystals. Zbl 1378.81031 Damanik, David; Embree, Mark; Gorodetski, Anton 41 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 29 2015 Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. Zbl 1358.37117 Damanik, David; Gorodetski, Anton; Solomyak, Boris 20 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 8 2015 Transport exponents of Sturmian Hamiltonians. Zbl 1323.82038 Damanik, David; Gorodetski, Anton; Liu, Qing-Hui; Qu, Yan-Hui 7 2015 Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian. Zbl 1310.81065 Damanik, David; Gorodetski, Anton 3 2015 Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians. Zbl 1327.47029 Damanik, David; Gorodetski, Anton 2 2015 On the inverse spectral problem for the quasi-periodic Schrödinger equation. Zbl 1296.35168 Damanik, David; Goldstein, Michael 23 2014 Dynamics of unitary operators. Zbl 1321.47076 Damanik, David; Fillman, Jake; Vance, Robert 20 2014 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089 Avila, Artur; Damanik, David; Zhang, Zhenghe 15 2014 Continuum Schrödinger operators associated with aperiodic subshifts. Zbl 1292.81052 Damanik, David; Fillman, Jake; Gorodetski, Anton 14 2014 Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications. Zbl 1291.33010 Damanik, David; Munger, Paul; Yessen, William N. 16 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. 14 2013 Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian. Zbl 1276.81059 Damanik, David; Gorodetski, Anton 8 2013 Limit-periodic Schrödinger operators on \(\mathbb Z^d\): uniform localization. Zbl 1285.35005 Damanik, David; Gan, Zheng 7 2013 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007 Avila, Artur; Bochi, Jairo; Damanik, David 19 2012 The density of states measure of the weakly coupled Fibonacci Hamiltonian. Zbl 1256.81035 Damanik, David; Gorodetski, Anton 12 2012 Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Zbl 1232.81016 Damanik, David; Gorodetski, Anton 34 2011 Spectral properties of limit-periodic Schrödinger operators. Zbl 1242.47023 Damanik, David; Gan, Zheng 17 2011 Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. Zbl 1314.47053 Damanik, David; Gan, Zheng 16 2011 A continuum version of the Kunz-Souillard approach to localization in one dimension. Zbl 1245.34084 Damanik, David; Stolz, Günter 5 2011 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031 Damanik, David; Killip, Rowan; Simon, Barry 60 2010 A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Zbl 1198.81085 Damanik, David; Tcheremchantsev, Serguei 18 2010 Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents. Zbl 1191.47058 Damanik, David; Gan, Zheng 13 2010 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012 Avila, Artur; Bochi, Jairo; Damanik, David 29 2009 Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian. Zbl 1154.82312 Damanik, David; Gorodetski, Anton 25 2009 The spectrum of the weakly coupled Fibonacci Hamiltonian. Zbl 1169.82009 Damanik, David; Gorodetski, Anton 11 2009 Schrödinger operators defined by interval-exchange transformations. Zbl 1184.81056 Chaika, Jon; Damanik, David; Krüger, Helge 5 2009 The repetition property for sequences on tori generated by polynomials or skew-shifts. Zbl 1186.37018 Boshernitzan, Michael; Damanik, David 4 2009 Almost everything about the Fibonacci operator. Zbl 1175.81090 Damanik, David 3 2009 Pinned repetitions in symbolic flows: preliminary results. Zbl 1184.37013 Boshernitzan, M.; Damanik, David 2 2009 Almost periodic Szegő cocycles with uniformly positive Lyapunov exponents. Zbl 1185.37063 Damanik, David; Krüger, Helge 1 2009 The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097 Damanik, David; Pushnitski, Alexander; Simon, Barry 116 2008 The fractal dimension of the spectrum of the Fibonacci Hamiltonian. Zbl 1192.81151 Damanik, D.; Embree, M.; Gorodetski, A.; Tcheremchantsev, S. 39 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 30 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 15 2008 Generic continuous spectrum for ergodic Schrödinger operators. Zbl 1159.35016 Boshernitzan, Michael; Damanik, David 14 2008 Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations. Zbl 1259.37011 Bjerklöv, Kristian; Damanik, David; Johnson, Russell 4 2008 Upper bounds in quantum dynamics. Zbl 1114.81036 Damanik, David; Tcheremchantsev, Serguei 32 2007 Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: a survey of Kotani theory and its applications. Zbl 1130.82018 Damanik, David 30 2007 Strictly ergodic subshifts and associated operators. Zbl 1130.82017 Damanik, David 23 2007 Unbounded Jacobi matrices at critical coupling. Zbl 1120.47020 Damanik, David; Naboko, Serguei 12 2007 Schrödinger operators with many bound states. Zbl 1114.34065 Damanik, David; Remling, Christian 11 2007 Uniform Szegő cocycles over strictly ergodic subshifts. Zbl 1108.37002 Damanik, David; Lenz, Daniel 8 2007 Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Zbl 1110.47019 Damanik, David; Teschl, Gerald 7 2007 A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem. Zbl 1118.37009 Damanik, David; Lenz, Daniel 35 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 27 2006 Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030 Damanik, David; Simon, Barry 22 2006 Substitution dynamical systems: characterization of linear repetitivity and applications. Zbl 1094.37007 Damanik, David; Lenz, Daniel 20 2006 Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Zbl 1122.47028 Damanik, David; Lenz, Daniel 19 2006 ...and 46 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 836 Authors 109 Damanik, David 36 Fillman, Jake 24 Simon, Barry 22 de Oliveira, César R. 21 Lenz, Daniel H. 19 Pelantová, Edita 18 Gorodetskii, Anton Semenovich 18 Stolz, Gunter 17 Jitomirskaya, Svetlana Yakovlevna 16 Avila, Artur 15 Lukic, Milivoje 15 Ong, Darren C. 14 Zhou, Qi 12 Román, Pablo Manuel 12 Yuditskii, Peter Meerovich 11 Liu, Qinghui 11 Shallit, Jeffrey Outlaw 11 Zamboni, Luca Quardo 10 Carvalho, Silas L. 10 Krüger, Helge 10 Zhang, Zhenghe 9 Choque Rivero, Abdon Eddy 9 Garza, Luis E. 9 Koelink, Erik 9 Marcellán Español, Francisco 9 Naboko, Serguei N. 9 Qu, Yanhui 9 Rampersad, Narad 9 You, Jiangong 8 Chulaevsky, Victor 8 Eichinger, Benjamin 8 Germinet, François 8 Han, Rui 8 Liu, Wencai 8 Masáková, Zuzana 8 Rouault, Alain 8 Salo, Ville O. 8 Zinchenko, Maxim 7 Beckus, Siegfried 7 Christiansen, Jacob Stordal 7 Duarte, Pedro 7 Fici, Gabriele 7 Fuentes, Edinson 7 Goldstein, Michael 7 Grünbaum, Francisco Alberto 7 Guo, Shuzheng 7 Killip, Rowan 7 Klein, Silvius 7 Mañas, Manuel 7 Nagel, Jan 7 Safronov, Oleg 7 Tcheremchantsev, Serguei 7 Velázquez, Luis 7 Yessen, William N. 7 Zhang, Shiwen 7 Zhao, Xin 6 Allouche, Jean-Paul Simon 6 Aloisio, Moacir 6 Boumaza, Hakim 6 Cai, Ao 6 Dvořáková, L’ubomíra 6 Frid, Anna Èduardovna 6 Gamboa, Fabrice 6 García-Ardila, Juan Carlos 6 Ge, Lingrui 6 Glen, Amy 6 Klein, Abel 6 Kozhan, Rostyslav V. 6 Last, Yoram 6 Marin, Laurent 6 Remling, Christian 6 Shi, Yunfeng 6 Shterenberg, Roman G. 6 Sims, Robert L. 6 Świderski, Grzegorz 6 Wang, Fengpeng 5 Baake, Michael 5 Bezerra, Jamerson 5 Bochi, Jairo 5 Breuer, Jonathan 5 Cassaigne, Julien 5 Cedzich, Christopher 5 Dette, Holger 5 Fang, Licheng 5 Gan, Zheng 5 Kachkovskiy, Ilya V. 5 Karpeshina, Yulia E. 5 Korotyaev, Evgeny L. 5 Lindner, Marko 5 Prado, Roberto A. 5 Solomyak, Boris 5 Starosta, Štěpán 5 Sukhtaiev, Selim 5 VandenBoom, Tom 5 Wen, Zhi-Ying 5 Werner, Albert H. 4 Ambrož, Petr 4 Balková, L’ubomíra 4 Bikchentaev, Aĭrat Midkhatovich 4 Bingham, Nicholas Hugh ...and 736 more Authors all top 5 Cited in 198 Serials 75 Communications in Mathematical Physics 45 Journal of Mathematical Physics 42 Journal of Functional Analysis 41 Theoretical Computer Science 35 Annales Henri Poincaré 31 Journal of Mathematical Analysis and Applications 28 Journal of Spectral Theory 26 Journal of Approximation Theory 24 Proceedings of the American Mathematical Society 21 Advances in Mathematics 20 Ergodic Theory and Dynamical Systems 17 Journal of Statistical Physics 17 Letters in Mathematical Physics 17 Duke Mathematical Journal 15 Reviews in Mathematical Physics 15 Constructive Approximation 14 Journal d’Analyse Mathématique 13 Transactions of the American Mathematical Society 12 European Journal of Combinatorics 11 Journal of the European Mathematical Society (JEMS) 10 Nonlinearity 9 Inventiones Mathematicae 9 Linear Algebra and its Applications 9 Journal of Dynamics and Differential Equations 9 Mathematical Physics, Analysis and Geometry 8 Integral Equations and Operator Theory 8 Journal of Differential Equations 8 RAIRO. 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Theoretical Informatics and Applications 2 Information Processing Letters 2 Mathematical Notes 2 Theoretical and Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Arkiv för Matematik 2 Acta Mathematica 2 Functional Analysis and its Applications 2 Journal of Multivariate Analysis 2 Journal of Statistical Planning and Inference 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Results in Mathematics 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Information and Computation 2 SIAM Journal on Matrix Analysis and Applications 2 SIAM Journal on Mathematical Analysis 2 Russian Journal of Mathematical Physics 2 St. Petersburg Mathematical Journal 2 Random Operators and Stochastic Equations 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Sbornik: Mathematics 2 Discrete Mathematics and Theoretical Computer Science. DMTCS 2 Journal of Integer Sequences 2 Communications in Nonlinear Science and Numerical Simulation 2 Dynamical Systems 2 Computational Methods and Function Theory ...and 98 more Serials all top 5 Cited in 53 Fields 393 Operator theory (47-XX) 248 Dynamical systems and ergodic theory (37-XX) 241 Quantum theory (81-XX) 179 Partial differential equations (35-XX) 152 Statistical mechanics, structure of matter (82-XX) 135 Computer science (68-XX) 126 Ordinary differential equations (34-XX) 107 Harmonic analysis on Euclidean spaces (42-XX) 79 Special functions (33-XX) 79 Difference and functional equations (39-XX) 76 Probability theory and stochastic processes (60-XX) 52 Linear and multilinear algebra; matrix theory (15-XX) 49 Number theory (11-XX) 44 Measure and integration (28-XX) 34 Functions of a complex variable (30-XX) 31 Functional analysis (46-XX) 24 Combinatorics (05-XX) 23 Convex and discrete geometry (52-XX) 20 Numerical analysis (65-XX) 15 Global analysis, analysis on manifolds (58-XX) 10 Group theory and generalizations (20-XX) 8 Real functions (26-XX) 8 Approximations and expansions (41-XX) 8 Integral transforms, operational calculus (44-XX) 8 Statistics (62-XX) 7 Topological groups, Lie groups (22-XX) 7 Mechanics of particles and systems (70-XX) 6 General and overarching topics; collections (00-XX) 6 Algebraic geometry (14-XX) 6 Abstract harmonic analysis (43-XX) 5 Associative rings and algebras (16-XX) 5 Potential theory (31-XX) 5 Sequences, series, summability (40-XX) 4 General topology (54-XX) 4 Optics, electromagnetic theory (78-XX) 3 Mathematical logic and foundations (03-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Nonassociative rings and algebras (17-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-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) Citations by Year