Publications

Selected Publications (Tier 1)

[154] Artur Avila, David Damanik, Zhenghe Zhang, Schrödinger operators with potentials generated by hyperbolic transformations: I. Positivity of the Lyapunov exponent, Invent. Math. 231 (2023), 851-927

[115] David Damanik, Michael Goldstein, Milivoje Lukic, The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations, Invent. Math. 207 (2017), 895-980

[111] David Damanik, Michael Goldstein, On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data, J. Amer. Math. Soc. 29 (2016), 825-856

[110] David Damanik, Anton Gorodetski, William Yessen, The Fibonacci Hamiltonian, Invent. Math. 206 (2016), 629-692

[93] David Damanik, Michael Goldstein, On the inverse spectral problem for the quasi-periodic Schrödinger equation, Publ. Math. Inst. Hautes Études Sci. 119 (2014), 217-401

[78] David Damanik, Rowan Killip, Barry Simon, Perturbations of orthogonal polynomials with periodic recursion coefficients, Ann. of Math. 171 (2010), 1931-2010

[66] Artur Avila, David Damanik, Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling, Invent. Math. 172 (2008), 439-453

[60] David Damanik, Serguei Tcheremchantsev, Upper bounds in quantum dynamics, J. Amer. Math. Soc. 20 (2007), 799-827

[52] David Damanik, Barry Simon, Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics, Invent. Math. 165 (2006), 1-50

[40] David Damanik, Rowan Killip, Half-line Schrödinger operators with no bound states, Acta Math. 193 (2004), 31-72

Selected Publications (Tier 2)

[153] Artur Avila, David Damanik, Anton Gorodetski, The spectrum of Schrödinger operators with randomly perturbed ergodic potentials, Geom. Funct. Anal. 33 (2023), 364-375

[119] Ilia Binder, David Damanik, Michael Goldstein, Milivoje Lukic, Almost periodicity in time of solutions of the KdV equation, Duke Math. J. 167 (2018), 2633-2678

[118] David Damanik, Michael Goldstein, Wilhelm Schlag, Mircea Voda, Homogeneity of the spectrum for quasi-periodic Schrödinger operators, J. Eur. Math. Soc. 20 (2018), 3073-3111

[100] David Damanik, Anton Gorodetski, Boris Solomyak, Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian, Duke Math. J. 164 (2015), 1603-1640

[84] Artur Avila, Jairo Bochi, David Damanik, Opening gaps in the spectrum of strictly ergodic Schrödinger operators, J. Eur. Math. Soc. 14 (2012), 61-106

[83] David Damanik, Anton Gorodetski, The density of states measure of the weakly coupled Fibonacci Hamiltonian, Geom. Funct. Anal. 22 (2012), 976-989

[75] Artur Avila, Jairo Bochi, David Damanik, Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts, Duke Math. J. 146 (2009), 253-280

[59] David Damanik, Christian Remling, Schrödinger operators with many bound states, Duke Math. J. 136 (2007), 51-80

[48] David Damanik, Daniel Lenz, A criterion of Boshernitzan and uniform convergence in the multiplicative ergodic theorem, Duke Math. J. 133 (2006), 95-123

[46] Artur Avila, David Damanik, Generic singular spectrum for ergodic Schrödinger operators, Duke Math. J. 130 (2005), 393-400

[21] David Damanik, Robert Sims, Günter Stolz, Localization for one-dimensional, continuum, Bernoulli-Anderson models, Duke Math. J. 114 (2002), 59-100

[18] David Damanik, Peter Stollmann, Multi-scale analysis implies strong dynamical localization, Geom. Funct. Anal. 11 (2001), 11-29

Books

[161] David Damanik, Jake Fillman, One-dimensional Ergodic Schrödinger Operators - II. Specific Classes, Graduate Studies in Mathematics 249, American Mathematical Society, Providence, RI, 2024  AMS  Amazon

[146] David Damanik, Jake Fillman, One-Dimensional Ergodic Schrödinger Operators, I. General Theory, Graduate Studies in Mathematics 221, American Mathematical Society, 2022  AMS  Amazon

Complete Publication List

[xii] David Damanik, Zhiyan Zhao, Ballistic transport for discrete multi-dimensional Schrödinger operators with decaying potential, arXiv:2507.04988 

[xi] Artur Avila, David Damanik, Dense phenomena for ergodic Schrödinger operators: I. Spectrum, integrated density of states, and Lyapunov exponent, arXiv:2506.14259

[x] David Damanik, Jake Fillman, Giorgio Young, Optimal dispersion for discrete periodic Schrödinger operators, arXiv:2505.14475

[ix] David Damanik, Anton Gorodetski, Victor Kleptsyn, Localization for random Schrödinger operators defined by block factors, arXiv:2504.08153

[viii] Ilia Binder, David Damanik, Michael Goldstein, Milivoje Lukić, Comb domains of Schrödinger operators with small quasiperiodic potentials, arXiv:2504.04200

[vii] David Damanik, Íris Emilsdóttir, Jake Fillman, Gap labels and asymptotic gap opening for full shifts, arXiv:2412.13391

[vi] David Damanik, Yong Li, Fei Xu, Existence, uniqueness and asymptotic dynamics of nonlinear Schrödinger equations with quasi-periodic initial data: II. The derivative NLS, arXiv:2406.02512

[v] David Damanik, Yong Li, Fei Xu, Existence, uniqueness and asymptotic dynamics of nonlinear Schrödinger equations with quasi-periodic initial data: I. The standard NLS, arXiv:2405.19583

[iv] David Damanik, Long Li, Opening gaps in the spectrum of strictly ergodic Jacobi and CMV matrices, arXiv:2404.03864

[iii] David Damanik, Tal Malinovitch, Giorgio Young, What is ballistic transport?, arXiv:2403.19618 

[ii] Artur Avila, David Damanik, Zhenghe Zhang, Schrödinger operators with potentials generated by hyperbolic transformations: II. Large deviations and Anderson localization, arXiv:2311.08612

[i] Adam Black, David Damanik, Tal Malinovitch, Giorgio Young, Directional ballistic transport for partially periodic Schrödinger operators, arXiv:2311.08612

[162] David Damanik, Daniel Lenz, Uniformity aspects of SL(2,R) cocycles and applications to Schrödinger operators defined over Boshernitzan subshifts, Ergodic Theory Dynam. Systems 45 (2025), 1734-1756

[161] David Damanik, Jake Fillman, One-dimensional Ergodic Schrödinger Operators - II. Specific Classes, Graduate Studies in Mathematics 249, American Mathematical Society, Providence, RI, 2024  AMS  Amazon

[160] David Damanik, Yong Li, Fei Xu, Local existence and uniqueness of spatially quasi-periodic solutions to the generalized KdV equation, J. Math. Pures Appl. 186 (2024), 251-302

[159] David Damanik, Yong Li, Fei Xu, The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line, J. Funct. Anal. 286 (2024), Paper No. 110238, 39 pp. 

[158] David Damanik, Gang Meng, Meirong Zhang, Zhe Zhou, The rotation number for the Schrödinger operator with α-norm almost periodic measures, Math. Z. 307 (2024), Paper No. 71, 27 pp. 

[157] David Damanik, Meirong Zhang, Zhe Zhou, The rotation number for almost periodic potentials with jump discontinuities and δ-interactions, Ann. Henri Poincaré 25 (2024), 1359-1397 

[156] David Damanik, Mark Embree, Jake Fillman, May Mei, Discontinuities of the integrated density of states for Laplacians associated with Penrose and Ammann-Beenker tilings, Exp. Math. 33 (2024), 588-610

[155] David Damanik, Mark Embree, Jake Fillman, Gap labels for zeros of the partition function of the 1D Ising model via the Schwartzman homomorphism, Indag. Math. (N.S.) 35 (2024), 813-836

[154] Artur Avila, David Damanik, Zhenghe Zhang, Schrödinger operators with potentials generated by hyperbolic transformations: I. Positivity of the Lyapunov exponent, Invent. Math. 231 (2023), 851-927

[153] Artur Avila, David Damanik, Anton Gorodetski, The spectrum of Schrödinger operators with randomly perturbed ergodic potentials, Geom. Funct. Anal. 33 (2023), 364-375

[152] David Damanik, Xianzhe Li, Jiangong You, Qi Zhou, Stability of spectral types of quasi-periodic Schrödinger operators with respect to perturbations by decaying potentials, Commun. Math. Phys. 403 (2023), 1069-1108

[151] David Damanik, Jake Fillman, The almost sure essential spectrum of the doubling map model is connected, Commun. Math. Phys. 400 (2023), 793-804.

[150] David Damanik, Íris Emilsdóttir, Jake Fillman, The Schwartzman group of an affine transformation, J. Spectr. Theory 13 (2023), 1281-1296. 

[149] David Damanik, Jake Fillman, Zhenghe Zhang, Johnson-Schwartzman gap labelling for ergodic Jacobi matrices, J. Spectr. Theory 13 (2023), 297-318

[148] David Damanik, Jake Fillman, Chunyi Wang, Thin spectra and singular continuous spectral measures for limit-periodic Jacobi matrices, Math. Nachr. 296 (2023), 4279-4297

[147] David Damanik, Jake Fillman, Gap labelling for discrete one-dimensional ergodic Schrödinger operators, From Complex Analysis to Operator Theory - A Panorama, 341-404, Oper. Theory Adv. Appl. 291, Birkhäuser/Springer, Cham, 2023

[146] David Damanik, Jake Fillman, One-Dimensional Ergodic Schrödinger Operators, I. General Theory, Graduate Studies in Mathematics 221, American Mathematical Society, 2022  AMS  Amazon

[145] David Damanik, Shuzheng Guo, Darren Ong, Simon's OPUC Hausdorff dimension conjecture, Math. Ann. 384 (2022), 247-283

[144] David Damanik, Anton Gorodetski, Must the spectrum of a random Schrödinger operator contain an interval?, Commun. Math. Phys. 393 (2022), 1583-1613.

[143] David Damanik, Long Li, Qi Zhou, Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients, Trans. Amer. Math. Soc. 375 (2022), 6093-6125

[142] David Damanik, Daniel Lenz, Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line, Israel J. Math. 247 (2022), 783-796

[141] David Damanik, Jake Fillman, Philipp Gohlke, Spectral characteristics of Schrödinger operators generated by product systems, J. Spectr. Theory 12 (2022), 1659–1718

[140] David Damanik, Jon Chaika, Jake Fillman, Philipp Gohlke, Zero measure spectrum for multi-frequency Schrödinger operators, J. Spectr. Theory 12 (2022), 573-590

[139] David Damanik, Long Li, Qi Zhou, Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients, J. Funct. Anal. 283 (2022), Paper No. 109709

[138] David Damanik, Shuzheng Guo, Darren Ong, Subordinacy theory for extended CMV matrices, Sci. China Math. 65 (2022), 539-558.

[137] David Damanik, Zhe Zhou, The rotation number for almost periodic Schrödinger operators with $\delta$-potentials, J. Dynam. Differential Equations 34 (2022), 155-177

[136] David Damanik, Benjamin Eichinger, Peter Yuditskii, Szego's theorem for canonical systems: the Arov gauge and a sum rule, J. Spectr. Theory 11 (2021), 1255-1277

[135] David Damanik, Michael Boshernitzan, Jake Fillman, Milivoje Lukic, Ergodic Schrödinger operators in the infinite measure setting, J. Spectr. Theory 11 (2021), 873--902

[134] David Damanik, Jake Fillman, Anton Gorodetski, Multidimensional Schrödinger operators whose spectrum features a half line and a Cantor set, J. Funct. Anal. 280 (2021), 108911, 38 pp

[133] David Damanik, Jake Fillman, Mark Helman, Jacob Kesten, Selim Sukhtaiev, Random Hamiltonians with arbitrary point interactions in one dimension, J. Differential Equations 282 (2021), 104-126

[132] David Damanik, Licheng Fang, Hyunkyu Jun, Schrödinger operators generated by locally constant functions on the Fibonacci subshift, Ann. Henri Poincaré 22 (2021), 1459-1498

[131] David Damanik, Lyapunov exponents: recent applications of Furstenberg's theorem in spectral theory, MATRIX Annals, MATRIX Book Ser. 4, Springer, Cham (2021), 685--689

[130] David Damanik, Jake Fillman, Selim Sukhtaiev, Localization for Anderson models on metric and discrete tree graphs, Math. Ann. 376 (2020), 1337-1393

[129] David Damanik, Licheng Fang, Shuzheng Guo, Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients, J. Funct. Anal. 279 (2020), 108803, 22 pp

[128] David Damanik, Zheng Gan, Helge Krüger, Limit-periodic Schrödinger operators with a discontinuous Lyapunov exponent, J. Funct. Anal. 279 (2020), 108565, 16 pp

[127] David Damanik, Licheng Fang, Selim Sukhtaiev, Zero measure and singular continuous spectra for quantum graphs, Ann. Henri Poincaré 21 (2020), 2167-2191

[126] David Damanik, Rafael del Rio, Asaf L. Franco, Random Sturm-Liouville operators with generalized point interactions, Oper. Matrices 14 (2020), 1101-1125

[125] Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang, Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent, Trans. Amer. Math. Soc. 372 (2019), 3619-3667

[124] Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang, Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly, J. Funct. Anal. 277 (2019), 3179-3186

[123] David Damanik, Selim Sukhtaiev, Anderson localization for radial tree graphs with random branching numbers, J. Funct. Anal. 277 (2019), 418-433

[122] David Damanik, Fengpeng Wang, Anderson localization for quasi-periodic CMV matrices and quantum walks, J. Funct. Anal. 276 (2019), 1978-2006

[121] David Damanik, Jake Fillman and Anton Gorodetski, Multidimensional almost-periodic Schrödinger operators with Cantor spectrum, Ann. Henri Poincaré 20 (2019), 1393-1402

[120] David Damanik, Jake Fillman, Limit-periodic Schrödinger operators with Lipschitz continuous IDS, Proc. Amer. Math. Soc. 147 (2019), 1531-1539

[119] Ilia Binder, David Damanik, Michael Goldstein, Milivoje Lukic, Almost periodicity in time of solutions of the KdV equation, Duke Math. J. 167 (2018), 2633-2678

[118] David Damanik, Michael Goldstein, Wilhelm Schlag, Mircea Voda, Homogeneity of the spectrum for quasi-periodic Schrödinger operators, J. Eur. Math. Soc. 20 (2018), 3073-3111

[117] David Damanik, Anton Gorodetski, Spectral transitions for the square Fibonacci Hamiltonian, J. Spectr. Theory 8 (2018), 1487-1507

[116] Ilia Binder, David Damanik, Milivoje Lukic, Tom VandenBoom, Almost-periodicity in time of solutions of the Toda lattice, C. R. Math. Rep. Acad. Sci. Canada 40 (2018), 1-28

[115] David Damanik, Michael Goldstein, Milivoje Lukic, The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations, Invent. Math. 207 (2017), 895-980

[114] David Damanik, Schrödinger operators with dynamically defined potentials, Ergodic Theory Dynam. Systems 37 (2017), 1681-1764

[113] David Damanik, Jake Fillman, Milivoje Lukic, Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum, J. Spectr. Theory 7 (2017), 1101-1118

[112] David Damanik, Michael Goldstein, Milivoje Lukic, A multi-scale analysis scheme on Abelian groups with an application to operators dual to Hill's equation, Trans. Amer. Math. Soc. 369 (2017), 1689-1755

[111] David Damanik, Michael Goldstein, On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data, J. Amer. Math. Soc. 29 (2016), 825-856

[110] David Damanik, Anton Gorodetski, William Yessen, The Fibonacci Hamiltonian, Invent. Math. 206 (2016), 629-692

[109] David Damanik, Anton Gorodetski, An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators, Adv. Math. 297 (2016), 149-173

[108] David Damanik, Peter Yuditskii, Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces, Adv. Math. 293 (2016), 738-781

[107] David Damanik, Jake Fillman, Darren Ong, Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices, J. Math. Pures Appl. 105 (2016), 293-341

[106] David Damanik, Marius Lemm, Milivoje Lukic, William Yessen, On anomalous Lieb-Robinson bounds for the Fibonacci XY chain, J. Spectr. Theory 6 (2016), 601-628

[105] David Damanik, Michael Goldstein, Milivoje Lukic, The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous, J. Spectr. Theory 6 (2016), 415-427

[104] David Damanik, Jon Erickson, Jake Fillman, Gerhardt Hinkle, Alan Vu, Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line, J. Approx. Theory 208 (2016), 59-84

[103] Michael Baake, David Damanik, Uwe Grimm, What is ... aperiodic order?, Notices Amer. Math. Soc. 63 (2016), 647-650

[102] David Damanik, Jake Fillman, Milivoje Lukic, William Yessen, Characterizations of uniform hyperbolicity and spectra of CMV matrices, Discrete Contin. Dyn. Syst. S 9 (2016), 1009-1023

[101] Faustin Adiceam, David Damanik, Franz Gähler, Uwe Grimm, Alan Haynes, Antoine Julien, Andrés Navas, Lorenzo Sadun Barak Weiss, Open problems and conjectures related to the theory of mathematical quasicrystals, Arnold Math. J. 2 (2016), 579-592

[100] David Damanik, Anton Gorodetski, Boris Solomyak, Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian, Duke Math. J. 164 (2015), 1603-1640

[99] David Damanik, Milivoje Lukic, William Yessen, Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems, Commun. Math. Phys. 337 (2015), 1535-1561

[98] David Damanik, Anton Gorodetski, Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians, Commun. Math. Phys. 337 (2015), 1241-1253

[97] David Damanik, Jake Fillman, Milivoje Lukic, William Yessen, Uniform hyperbolicity for Szego cocycles and applications to random CMV matrices and the Ising model, Int. Math. Res. Not. 2015 (2015), 7110-7129

[96] David Damanik, Anton Gorodetski, Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian, Israel J. Math. 206 (2015), 109-126

[95] David Damanik, Anton Gorodetski, Qinghui Liu, Yanhui Qu, Transport exponents of Sturmian Hamiltonians, J. Funct. Anal. 269 (2015), 1404-1440

[94] David Damanik, Anton Gorodetski, Mark Embree, Spectral properties of Schrödinger operators arising in the study of quasicrystals, Mathematics of Aperiodic Order, Birkhäuser/Springer (2015), 307-370

[93] David Damanik, Michael Goldstein, On the inverse spectral problem for the quasi-periodic Schrödinger equation, Publ. Math. Inst. Hautes Études Sci. 119 (2014), 217-401

[92] Artur Avila, David Damanik, Zhenghe Zhang, Singular density of states measure for subshift and quasi-periodic Schrödinger operators, Commun. Math. Phys. 330 (2014), 469-498

[91] David Damanik, Marius Lemm, Milivoje Lukic William Yessen, New anomalous Lieb-Robinson bounds in quasiperiodic XY chains, Phys. Rev. Lett. 113 (2014), 127202

[90] David Damanik, Jake Fillman, Robert Vance, Dynamics of unitary operators, J. Fractal Geom. 1 (2014), 391-425

[89] David Damanik, Jake Fillman, Anton Gorodetski, Continuum Schrödinger operators associated with aperiodic subshifts, Ann. Henri Poincaré 15 (2014), 1123-1144 (This paper was awarded the  2014 Annales Henri Poincaré Prize.)

[88] David Damanik, Anton Gorodetski, Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian, Commun. Math. Phys. 323 (2013), 497-515

[87] David Damanik, Zheng Gan, Limit-periodic Schrödinger operators on Z^d: Uniform localization, J. Funct. Anal. 265 (2013), 435-448

[86] David Damanik, Paul Munger, William Yessen, Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, I. The essential support of the measure, J. Approx. Theory 173 (2013), 56-88

[85] David Damanik, Paul Munger, William Yessen, Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, II. Applications, J. Stat. Phys. 153 (2013), 339-362

[84] Artur Avila, Jairo Bochi, David Damanik, Opening gaps in the spectrum of strictly ergodic Schrödinger operators, J. Eur. Math. Soc. 14 (2012), 61-106

[83] David Damanik, Anton Gorodetski, The density of states measure of the weakly coupled Fibonacci Hamiltonian, Geom. Funct. Anal. 22 (2012), 976-989

[82] David Damanik, Anton Gorodetski, Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian, Commun. Math. Phys. 305 (2011), 221-277

[81] David Damanik, Günter Stolz, A continuum version of the Kunz-Souillard approach to localization in one dimension, J. Reine Angew. Math. 660 (2011), 99-130

[80] David Damanik, Zheng Gan, Limit-periodic Schrödinger operators with uniformly localized eigenfunctions, J. d'Analyse Math. 115 (2011), 33-49

[79] David Damanik, Zheng Gan, Spectral properties of limit-periodic Schrödinger operators, Commun. Pure Appl. Anal. 10 (2011), 859-871

[78] David Damanik, Rowan Killip, Barry Simon, Perturbations of orthogonal polynomials with periodic recursion coefficients, Ann. of Math. 171 (2010), 1931-2010

[77] David Damanik, Zheng Gan, Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents, J. Funct. Anal. 258 (2010), 4010-4025

[76] David Damanik, Serguei Tcheremchantsev, A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators, Discrete Contin. Dyn. Syst. A 28 (2010), 1381-1412

[75] Artur Avila, Jairo Bochi, David Damanik, Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts, Duke Math. J. 146 (2009), 253-280

[74] Michael Boshernitzan, David Damanik, The repetition property for sequences on tori generated by polynomials or skew-shifts, Israel J. Math. 174 (2009), 189-202

[73] Jon Chaika, David Damanik, Helge Krüger, Schrödinger operators defined by interval exchange transformations, J. Mod. Dyn. 3 (2009), 253-270

[72] David Damanik, Helge Krüger, Almost periodic Szegö cocycles with uniformly positive Lyapunov exponents, J. Approx. Theory 161 (2009), 813-818

[71] David Damanik, Anton Gorodetski, Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian, Nonlinearity 22 (2009), 123--143

[70] David Damanik, Quantum dynamical applications of Salem's theorem (with Rafael del Rio), Lett. Math. Phys. 22 (2009), 13-19

[69] David Damanik, Anton Gorodetski, The spectrum of the weakly coupled Fibonacci Hamiltonian, Electron. Res. Announc. Math. Sci. 16 (2009), 23-29

[68] David Damanik, Almost everything about the Fibonacci operator, New Trends in Mathematical Physics, Selected contributions of the XVth International Congress on Mathematical Physics, Springer (2009), 149-159

[67] Michael Boshernitzan, David Damanik, Pinned repetitions in symbolic flows: preliminary results, Discrete Contin. Dyn. Syst. 2009, Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference, suppl. (2009), 869-878

[66] Artur Avila, David Damanik, Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling, Invent. Math. 172 (2008), 439-453

[65] Michael Boshernitzan, David Damanik, Generic continuous spectrum for ergodic Schrödinger operators, Commun. Math. Phys. 283 (2008), 647-662

[64] David Damanik, Mark Embree, Anton Gorodetski, and Serguei Tcheremchantsev, The fractal dimension of the spectrum of the Fibonacci Hamiltonian, Commun. Math. Phys. 280 (2008), 499-516

[63] David Damanik, Alexander Pushnitski, Barry Simon, The analytic theory of matrix orthogonal polynomials, Surv. Approx. Theory 4 (2008), 1-85

[62] David Damanik, Serguei Tcheremchantsev, Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian,  J. Funct. Anal. 255 (2008), 2872-2887

[61] David Damanik, Kristian Bjerklöv, Russell Johnson, Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations, Ann. Mat. Pura Appl. 187 (2008), 1-6

[60] David Damanik, Serguei Tcheremchantsev, Upper bounds in quantum dynamics, J. Amer. Math. Soc. 20 (2007), 799-827

[59] David Damanik, Christian Remling, Schrödinger operators with many bound states, Duke Math. J. 136 (2007), 51-80

[58] David Damanik, Sergey Naboko, Unbounded Jacobi matrices at critical coupling, J. Approx. Theory 145 (2007), 221-236

[57] David Damanik, Daniel Lenz, Uniform Szegö cocycles over strictly ergodic subshifts, J. Approx. Theory  144 (2007), 133-138

[56] David Damanik, Gerald Teschl, Bound states of discrete Schrödinger operators with super-critical inverse square potentials, Proc. Amer. Math. Soc. 135 (2007), 1123-1127

[55] David Damanik, Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, 539--563, Proc. Sympos. Pure Math., 76, Part 2, Amer. Math. Soc., Providence, RI, 2007

[54] David Damanik, Strictly ergodic subshifts and associated operators, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, 505--538, Proc. Sympos. Pure Math., 76, Part 2, Amer. Math. Soc., Providence, RI, 2007

[53] David Damanik, Barry Simon, Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity, Int. Math. Res. Not. (2006), Article ID 19396, 1-32

[52] David Damanik, Barry Simon, Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics, Invent. Math. 165 (2006), 1-50

[51] David Damanik, Daniel Lenz, Günter Stolz, Lower transport bounds for one-dimensional continuum Schrödinger operators, Math. Ann. 336 (2006), 361-389

[50] David Damanik, Verblunsky coefficients with Coulomb-type decay, J. Approx. Theory, 139 (2006), 257-268  

[49] David Damanik, Daniel Lenz, Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials, J. Math. Pures Appl. 85 (2006), 671-686

[48] David Damanik, Daniel Lenz, A criterion of Boshernitzan and uniform convergence in the multiplicative ergodic theorem, Duke Math. J. 133 (2006), 95-123

[47] David Damanik, Daniel Lenz, Substitution dynamical systems: characterization of linear repetitivity and applications, J. Math. Anal. Appl. 321 (2006), 766-780

[46] Artur Avila, David Damanik, Generic singular spectrum for ergodic Schrödinger operators, Duke Math. J. 130 (2005), 393-400

[45] David Damanik, Serguei Tcheremchantsev, Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading, J. d'Analyse Math. 97 (2005), 103-131

[44] David Damanik, Rowan Killip, Barry Simon, Schrödinger operators with few bound states,  Commun. Math. Phys. 258 (2005), 741-750

[43] David Damanik, Rowan Killip, Almost everywhere positivity of the Lyapunov exponent for the doubling map, Commun. Math. Phys. 257 (2005), 287-290

[42] David Damanik, Rowan Killip, Ergodic potentials with a discontinuous sampling function are non-deterministic, Math. Res. Lett. 12 (2005), 187-192

[41] David Damanik, Dynamical upper bounds for one-dimensional quasicrystals, J. Math. Anal. Appl. 303 (2005), 327-341

[40] David Damanik, Rowan Killip, Half-line Schrödinger operators with no bound states, Acta Math. 193 (2004), 31-72

[39] David Damanik, András Sütö, Serguei Tcheremchantsev, Power-law bounds on transfer matrices and quantum dynamics in one dimension, II, J. Funct. Anal. 216 (2004), 362-387

[38] David Damanik, Rowan Killip, Barry Simon, Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators, Int. Math. Res. Not. (2004), no. 22, 1087-1097

[37] David Damanik, Robert Sims, Günter Stolz, Localization for discrete one-dimensional random word models, J. Funct. Anal. 208 (2004), 423-445

[36] David Damanik, A version of Gordon's theorem for multi-dimensional Schrödinger operators, Trans. Amer. Math. Soc. 356 (2004), 495-507

[35] David Damanik, Daniel Lenz, Half-line eigenfunction estimates and singular continuous spectrum of zero Lebesgue measure, Forum Math. 16 (2004), 109-128

[34] David Damanik, Dirk Hundertmark, Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 132 (2004), 1957-1962

[33] Jean-Paul Allouche, Michael Baake, David Damanik, Julien Cassaigne, Palindrome complexity, Theoret. Comput. Sci. 292 (2003), 9-31

[32] David Damanik, Daniel Lenz, Powers in Sturmian sequences, European J. Combin. 24 (2003), 377-390

[31] David Damanik, Michael Landrigan, Log-dimensional spectral properties of one-dimensional quasicrystals, Proc. Amer. Math. Soc. 131 (2003), 2209-2216

[30] David Damanik, Serguei Tcheremchantsev, Power-law bounds on transfer matrices and quantum dynamics in one dimension, Commun. Math. Phys. 236 (2003), 513-534

[29] David Damanik, Dirk Hundertmark, Rowan Killip, Barry Simon, Variational estimates for discrete Schrödinger operators with potentials of indefinite sign, Commun. Math. Phys. 238 (2003), 545-562

[28] David Damanik, Daniel Lenz, Uniform spectral properties of one-dimensional quasicrystals, IV. Quasi-Sturmian potentials, J. d'Analyse Math. 90 (2003), 115-139

[27] David Damanik, Quantum dynamical bounds for one-dimensional quasicrystals, Contemp. Math. 327 (2003), 87-97

[26] David Damanik, Luca Q. Zamboni, Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators, Rev. Math. Phys. 15 (2003), 745-763

[25] David Damanik, Dirk Hundertmark, Barry Simon, Bound states and the Szegö condition for Jacobi matrices and Schrödinger operators,  J. Funct. Anal. 205 (2003), 357-379

[24] David Damanik, Daniel Lenz, The index of Sturmian sequences, European J. Combin. 23 (2002), 23-29

[23] David Damanik, Boris Solomyak, Some high-complexity Hamiltonians with purely singular continuous spectrum,  Ann. Henri Poincare 3 (2002), 99-105

[22] David Damanik, Robert Sims, Günter Stolz, Lyapunov exponents in continuum Bernoulli-Anderson models, Operator Theory: Advances and Applications 132, Birkhäuser, Basel (2002), pp. 121-130

[21] David Damanik, Robert Sims, Günter Stolz, Localization for one-dimensional, continuum, Bernoulli-Anderson models, Duke Math. J. 114 (2002), 59-100

[20] David Damanik, Absence of eigenvalues for a class of Schrödinger operators on the strip, Forum Math. 14 (2002), 797-806.

[19] Boris Adamczewski, David Damanik, Linearly recurrent circle map subshifts and an application to Schrödinger operators, Ann. Henri Poincare 3 (2002), 1019-1047

[18] David Damanik, Peter Stollmann, Multi-scale analysis implies strong dynamical localization, Geom. Funct. Anal. 11 (2001), 11-29

[17] David Damanik, Uniform singular continuous spectrum for the period doubling Hamiltonian, Ann. Henri Poincare 2 (2001), 101-108

[16] David Damanik, Spectral theory of Schrödinger operators with low-complexity potentials, Ferroelectrics 250 (2001), 143-149

[15] David Damanik, Daniel Lenz, Linear repetitivity, I. Uniform subadditive ergodic theorems and applications, Discrete Comput. Geom. 26 (2001), 411-428

[14] David Damanik, Jean-Michel Ghez, Laurent Raymond, A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians, Ann. Henri Poincare 2 (2001), 927-939

[13] David Damanik, Local symmetries in the period doubling sequence, Discrete Appl. Math. 100 (2000), 115-121

[12] David Damanik, Günter Stolz, A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators, Electron. J. Diff. Eqns. 2000 (2000), No. 55, pp. 1-8

[11] David Damanik, Douglas Zare, Palindrome complexity bounds for primitive substitution sequences, Discrete Math. 222 (2000), 259-267

[10] David Damanik, Substitution Hamiltonians with bounded trace map orbits, J. Math. Anal. Appl. 249 (2000), 393-411

[9] David Damanik, Gordon-type arguments in the spectral theory of one-dimensional quasicrystals, in Directions in Mathematical Quasicrystals, M. Baake, R. V. Moody, eds., CRM Monograph Series 13, AMS, Providence, RI (2000), pp. 277-304

[8] David Damanik, Rowan Killip, Reflection symmetries of almost periodic functions, J. Funct. Anal. 178 (2000), 251-257

[7] David Damanik, Singular continuous spectrum for a class of substitution Hamiltonians II., Lett. Math. Phys. 54 (2000), 25-31

[6] David Damanik, Rowan Killip, Daniel Lenz, Uniform spectral properties of one-dimensional quasicrystals, III. alpha-continuity, Commun. Math. Phys. 212 (2000), 191-204

[5] David Damanik, Daniel Lenz, Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent, Lett. Math. Phys. 50 (1999), 245-257

[4] David Damanik, Daniel Lenz, Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues, Commun. Math. Phys. 207 (1999), 687-696

[3] David Damanik, Singular continuous spectrum for a class of substitution Hamiltonians, Lett. Math. Phys. 46 (1998), 303-311

[2] David Damanik, Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure, Commun. Math. Phys. 196 (1998), 477-483

[1] David Damanik, alpha-continuity properties of one-dimensional quasicrystals, Commun. Math. Phys. 192 (1998), 169-182