Edit Profile (opens in new tab) Schlag, Wilhelm Compute Distance To: Compute Author ID: schlag.wilhelm Published as: Schlag, Wilhelm; Schlag, W. Documents Indexed: 104 Publications since 1991, including 6 Books 2 Contributions as Editor · 1 Further Contribution Co-Authors: 49 Co-Authors with 86 Joint Publications 1,587 Co-Co-Authors all top 5 Co-Authors 21 single-authored 15 Krieger, Joachim 10 Goldstein, Michael 10 Nakanishi, Kenji 8 Kenig, Carlos Eduardo 7 Donninger, Roland 7 Lawrie, Andrew G. W. 6 Soffer, Avraham 5 Erdoğan, Mehmet Burak 4 Côte, Raphaël 4 Goldberg, Michael Joseph 4 Liu, Baoping 4 Peres, Yuval 3 Bourgain, Jean 3 Costin, Ovidiu 3 Han, Rui 3 Rodnianski, Igor 3 Staubach, Wolfgang 3 Tataru, Daniel 3 Voda, Mircea 2 Beceanu, Marius 2 Deift, Percy A. 2 Galvez, Cherie 2 Gesztesy, Fritz 2 Huang, Min 2 Konyagin, Sergeĭ Vladimirovich 2 Lemm, Marius 2 Lindenstrauss, Elon 2 Muscalu, Camil 2 Perry, Peter A. 2 Tanveer, Saleh 2 Xu, Guixiang 1 Burq, Nicolas 1 Costin, Rodica D. 1 Creek, Matthew 1 Damanik, David 1 Daubechies, Ingrid Chantal 1 Delbaen, Freddy 1 Demanet, Laurent 1 Guth, Lawrence David 1 Ionescu, Alexandru D. 1 Jitomirskaya, Svetlana Yakovlevna 1 Killip, Rowan 1 Kontorovich, Alex V. 1 Lindblad, Hans 1 Lührmann, Jonas 1 Milman, Vitali D. 1 Mockenhaupt, Gerd 1 Park, Hyejin 1 Pisier, Gilles 1 Raugel, Geneviève 1 Rudnick, Zeév 1 Ruzsa, Imre Z. 1 Sarnak, Peter Clive 1 Shubin, C. 1 Snelson, Stanley 1 Sogge, Christopher D. 1 Solomyak, Boris 1 Staffilani, Gigliola 1 Tao, Terence 1 Varjú, Péter Pál 1 Wolff, Thomas H. all top 5 Serials 9 Communications in Mathematical Physics 7 American Journal of Mathematics 6 IMRN. International Mathematics Research Notices 5 Advances in Mathematics 4 Journal d’Analyse Mathématique 4 Duke Mathematical Journal 3 Nonlinearity 3 Inventiones Mathematicae 3 Journal of Functional Analysis 3 Transactions of the American Mathematical Society 3 Geometric and Functional Analysis. GAFA 3 Annals of Mathematics. Second Series 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Spectral Theory 2 Mathematische Annalen 2 Journal of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Cambridge Studies in Advanced Mathematics 2 Proceedings of Symposia in Pure Mathematics 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Physics 1 Acta Mathematica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Journal of Differential Equations 1 Journal of Number Theory 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Forum Mathematicum 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Calculus of Variations and Partial Differential Equations 1 Mathematical Research Letters 1 Annales Henri Poincaré 1 Moscow Mathematical Journal 1 Dynamics of Partial Differential Equations 1 Graduate Studies in Mathematics 1 Journal of Modern Dynamics 1 Analysis & PDE 1 Wiadomości Matematyczne 1 Zurich Lectures in Advanced Mathematics 1 EMS Monographs in Mathematics all top 5 Fields 69 Partial differential equations (35-XX) 29 Quantum theory (81-XX) 23 Operator theory (47-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 13 Dynamical systems and ergodic theory (37-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Probability theory and stochastic processes (60-XX) 5 Difference and functional equations (39-XX) 5 Relativity and gravitational theory (83-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Number theory (11-XX) 3 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 3 Abstract harmonic analysis (43-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 2,642 times in 1,387 Documents Cited by ▼ Year ▼ Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Zbl 1063.35035Rodnianski, Igor; Schlag, Wilhelm 142 2004 Sixty years of Bernoulli convolutions. Zbl 0961.42006Peres, Yuval; Schlag, Wilhelm; Solomyak, Boris 141 2000 Renormalization and blow up for charge one equivariant critical wave maps. Zbl 1139.35021Krieger, J.; Schlag, W.; Tataru, D. 102 2008 Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions. Zbl 0990.39014Goldstein, Michael; Schlag, Wilhelm 97 2001 Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions. Zbl 0961.42007Peres, Yuval; Schlag, Wilhelm 91 2000 Dispersive estimates for Schrödinger operators in dimensions one and three. Zbl 1086.81077Goldberg, M.; Schlag, W. 84 2004 Classical and multilinear harmonic analysis. Volume I. Zbl 1281.42002Muscalu, Camil; Schlag, Wilhelm 82 2013 Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation. Zbl 1170.35066Krieger, Joachim; Schlag, Wilhelm; Tataru, Daniel 81 2009 Dispersive estimates for Schrödinger operators: a survey. Zbl 1143.35001Schlag, W. 79 2007 Invariant manifolds and dispersive Hamiltonian evolution equations. Zbl 1235.37002Nakanishi, Kenji; Schlag, Wilhelm 62 2011 Concentration compactness for critical wave maps. Zbl 1387.35006Krieger, Joachim; Schlag, Wilhelm 54 2012 Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension. Zbl 1281.35077Krieger, J.; Schlag, W. 52 2006 Dispersive analysis of charge transfer models. Zbl 1130.81053Rodnianski, Igor; Schlag, Wilhelm; Soffer, Avraham 51 2005 On pointwise decay of linear waves on a Schwarzschild black hole background. Zbl 1242.83054Donninger, Roland; Schlag, Wilhelm; Soffer, Avy 50 2012 Classical and multilinear harmonic analysis. Volume II. Zbl 1282.42001Muscalu, Camil; Schlag, Wilhelm 49 2013 Dispersive estimates for Schrödinger operators in dimension two. Zbl 1134.35321Schlag, W. 48 2005 Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 46 2001 Global dynamics above the ground state energy for the cubic NLS equation in 3D. Zbl 1237.35148Nakanishi, K.; Schlag, W. 45 2012 Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues. Zbl 1171.82011Goldstein, Michael; Schlag, Wilhelm 43 2008 On the focusing critical semi-linear wave equation. Zbl 1219.35144Krieger, J.; Schlag, W. 42 2007 Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions. Zbl 1181.35208Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm 41 2009 Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 40 2002 Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Zbl 1180.35490Schlag, Wilhelm 37 2009 A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta. Zbl 1205.83041Donninger, Roland; Schlag, Wilhelm; Soffer, Avy 36 2011 Global dynamics away from the ground state for the energy-critical nonlinear wave equation. Zbl 1307.35170Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 35 2013 Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in \(\mathbb R^3\). Zbl 1152.35021Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm 35 2008 Characterization of large energy solutions of the equivariant wave map problem. I. Zbl 1315.35130Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 34 2015 A limiting absorption principle for the three-dimensional Schrödinger equation with \(L^p\) potentials. Zbl 1069.35063Goldberg, M.; Schlag, W. 34 2004 Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I. Zbl 1080.35102Erdoğan, M. Burak; Schlag, Wilhelm 31 2004 Agmon-Kato-Kuroda theorems for a large class of perturbations. Zbl 1092.35073Ionescu, Alexandru D.; Schlag, Wilhelm 31 2006 Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II. Zbl 1146.35324Erdoğan, M. Burak; Schlag, Wilhelm 31 2006 Center-stable manifold of the ground state in the energy space for the critical wave equation. Zbl 1315.35133Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 30 2015 Full range of blow up exponents for the quintic wave equation in three dimensions. Zbl 1320.35096Krieger, Joachim; Schlag, Wilhelm 30 2014 Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation. Zbl 1213.35307Nakanishi, K.; Schlag, W. 29 2011 Non-generic blow-up solutions for the critical focusing NLS in 1-D. Zbl 1163.35035Krieger, J.; Schlag, Wilhelm 28 2009 Characterization of large energy solutions of the equivariant wave map problem. II. Zbl 1315.35131Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 26 2015 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 26 1997 Anderson localization for Schrödinger operators on \(\mathbb{Z}\) with strongly mixing potentials. Zbl 1040.81014Bourgain, Jean; Schlag, Wilhelm 26 2000 On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations. Zbl 1268.82013Goldstein, Michael; Schlag, Wilhelm 25 2011 Renormalization and blow up for the critical Yang-Mills problem. Zbl 1183.35203Krieger, J.; Schlag, W.; Tataru, D. 25 2009 Global dynamics of the nonradial energy-critical wave equation above the ground state energy. Zbl 1272.35153Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 25 2013 Schauder and \(L^ p\) estimates for parabolic systems via Campanato spaces. Zbl 0864.35023Schlag, Wilhelm 25 1996 A generalization of Bourgain’s circular maximal theorem. Zbl 0867.42010Schlag, W. 24 1997 Decay for the wave and Schrödinger evolutions on manifolds with conical ends. I. Zbl 1185.35046Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang 22 2010 Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation. Zbl 1106.35044Demanet, Laurent; Schlag, Wilhelm 21 2006 Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption. Zbl 1256.35138Nakanishi, K.; Schlag, W. 21 2012 Relaxation of wave maps exterior to a ball to harmonic maps for all data. Zbl 1288.35356Kenig, Carlos E.; Lawrie, Andrew; Schlag, Wilhelm 21 2014 Spectral theory and nonlinear partial differential equations: a survey. Zbl 1121.35121Schlag, Wilhelm 20 2006 Threshold phenomenon for the quintic wave equation in three dimensions. Zbl 1297.35139Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 20 2014 Exotic blowup solutions for the \(u^5\) focusing wave equation in \(\mathbb{R}^{3}\). Zbl 1310.35170Donninger, Roland; Huang, Min; Krieger, Joachim; Schlag, Wilhelm 19 2014 On the spectral properties of \(L_{\pm }\) in three dimensions. Zbl 1232.35106Costin, Ovidiu; Huang, Min; Schlag, Wilhelm 17 2012 Channels of energy for the linear radial wave equation. Zbl 1331.35209Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm 17 2015 Energy partition for the linear radial wave equation. Zbl 1311.35022Côte, Raphaël; Kenig, Carlos E.; Schlag, Wilhelm 16 2014 Decay for the wave and Schrödinger evolutions on manifolds with conical ends. II. Zbl 1187.35032Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang 15 2010 Global dynamics above the ground state energy for the one-dimensional NLKG equation. Zbl 1263.35002Krieger, J.; Nakanishi, K.; Schlag, W. 14 2012 Profiles for the radial focusing \(4d\) energy-critical wave equation. Zbl 1404.35294Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 13 2018 Two Erdős problems on lacunary sequences: chromatic number and Diophantine approximation. Zbl 1215.05074Peres, Yuval; Schlag, Wilhelm 13 2010 Stable soliton resolution for exterior wave maps in all equivariance classes. Zbl 1331.35076Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm 13 2015 Classical and quantum scattering for a class of long range random potentials. Zbl 1019.81059Rodnianski, Igor; Schlag, Wilhelm 12 2003 Long time dynamics for damped Klein-Gordon equations. (Dynamique en temps grand des solutions de l’équation de Klein-Gordon amortie.) Zbl 1392.35041Burq, Nicolas; Raugel, Geneviève; Schlag, Wilhelm 12 2017 Scattering for wave maps exterior to a ball. Zbl 1264.35045Lawrie, A.; Schlag, W. 12 2013 Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle. Zbl 0949.42006Konyagin, S. V.; Schlag, W. 12 1999 Large global solutions for energy supercritical nonlinear wave equations on \(\mathbb{R}^{3+1}\). Zbl 1402.35180Krieger, Joachim; Schlag, Wilhelm 11 2017 Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Zbl 1321.37023Schlag, Wilhelm 11 2013 A geometric proof of the circular maximal theorem. Zbl 0942.42010Schlag, W. 10 1998 Decay estimates for the one-dimensional wave equation with an inverse power potential. Zbl 1241.35018Donninger, Roland; Schlag, Wilhelm 9 2010 Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation. Zbl 1244.35018Donninger, R.; Schlag, W. 9 2011 Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation. Zbl 1261.35037Nakanishi, K.; Schlag, W. 9 2012 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 8 2018 On continuum incidence problems related to harmonic analysis. Zbl 1043.42010Schlag, W. 8 2003 Structure formulas for wave operators. Zbl 1445.35234Beceanu, M.; Schlag, W. 7 2020 A course in complex analysis and Riemann surfaces. Zbl 1326.30003Schlag, Wilhelm 7 2014 On the integrated density of states for Schrödinger operators on \(\mathbb Z^2\) with quasi periodic potential. Zbl 1031.82023Schlag, Wilhelm 6 2001 Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials. Zbl 1160.35056Costin, Ovidiu; Schlag, Wilhelm; Staubach, Wolfgang; Tanveer, Saleh 6 2008 Structure formulas for wave operators under a small scaling invariant condition. Zbl 1428.35254Beceanu, Marius; Schlag, Wilhelm 6 2019 On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling. Zbl 07088060Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 6 2019 Frequency concentration and location lengths for the Anderson model at small disorders. Zbl 1032.60060Schlag, W.; Shubin, C.; Wolff, Thomas H. 6 2002 A remark on Littlewood-Paley theory for the distorted Fourier transform. Zbl 1159.42008Schlag, W. 5 2007 On the Hardy-Littlewood majorant problem for random sets. Zbl 1158.42002Mockenhaupt, G.; Schlag, W. 5 2009 Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base. Zbl 1471.35105Han, R.; Lemm, M.; Schlag, W. 5 2020 Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials. Zbl 1258.81038Costin, Ovidiu; Donninger, Roland; Schlag, Wilhelm; Tanveer, Saleh 5 2012 A geometric inequality with applications to the Kakeya problem in three dimensions. Zbl 0939.42012Schlag, W. 5 1998 Spectral theory and mathematical physics. A festschrift in honor of Barry Simon’s 60th birthday. Ergodic Schrödinger operators, singular spectrum, orthogonal polynomials, and inverse spectral theory. Based on the SimonFest conference, Pasadena, CA, USA, March 27–31, 2006. Zbl 1110.00015 4 2007 Bernoulli convolutions and an intermediate value theorem for entropies of \(k\)-partitions. Zbl 1024.37004Lindenstrauss, Elon; Peres, Yuval; Schlag, Wilhelm 4 2002 Linear stability of the Skyrmion. Zbl 1405.83018Creek, Matthew; Donninger, Roland; Schlag, Wilhelm; Snelson, Stanley 3 2017 Generic and non-generic behavior of solutions to defocusing energy critical wave equation with potential in the radial case. Zbl 1405.35114Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang 3 2017 On Schrödinger operators with dynamically defined potentials. Zbl 1143.47301Goldstein, Michael; Schlag, Wilhelm 3 2005 Energy growth in Schrödinger’s equation with Markovian forcing. Zbl 1033.81023Erdoğan, M. Burak; Killip, Rowan; Schlag, Wilhelm 3 2003 On pointwise decay of waves. Zbl 1467.81039Schlag, W. 3 2021 Global center stable manifold for the defocusing energy critical wave equation with potential. Zbl 1465.35306Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang 3 2020 The Weber equation as a normal form with applications to top of the barrier scattering. Zbl 1414.34067Costin, Rodica D.; Park, Hyejin; Schlag, Wilhelm 2 2018 On discrete Schrödinger operators with stochastic potentials. Zbl 1119.39302Schlag, W. 2 2005 \(L^p\to L^q\) estimates for the circular maximal function. Zbl 0981.42012Schlag, Wilhelm 2 2000 A higher-dimensional Bourgain-Dyatlov fractal uncertainty principle. Zbl 1439.32082Han, Rui; Schlag, Wilhelm 2 2020 An introduction to multiscale techniques in the theory of Anderson localization. I. Zbl 07515361Schlag, Wilhelm 2 2022 Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle. Zbl 1476.37074Han, Rui; Lemm, Marius; Schlag, Wilhelm 2 2020 On the formation of gaps in the spectrum of Schrödinger operators with quasi-periodic potentials. Zbl 1208.82027Goldstein, Michael; Schlag, Wilhelm 1 2007 Semilinear wave equations. Zbl 1373.35181Schlag, Wilhelm 1 2014 On uniformly distributed dilates of finite integer sequences. Zbl 0946.11016Konyagin, S. V.; Ruzsa, I. Z.; Schlag, W. 1 2000 On minima of the absolute value of certain random exponential sums. Zbl 0964.60012Schlag, W. 1 2000 An introduction to multiscale techniques in the theory of Anderson localization. I. Zbl 07515361Schlag, Wilhelm 2 2022 On pointwise decay of waves. Zbl 1467.81039Schlag, W. 3 2021 Structure formulas for wave operators. Zbl 1445.35234Beceanu, M.; Schlag, W. 7 2020 Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base. Zbl 1471.35105Han, R.; Lemm, M.; Schlag, W. 5 2020 Global center stable manifold for the defocusing energy critical wave equation with potential. Zbl 1465.35306Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang 3 2020 A higher-dimensional Bourgain-Dyatlov fractal uncertainty principle. Zbl 1439.32082Han, Rui; Schlag, Wilhelm 2 2020 Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle. Zbl 1476.37074Han, Rui; Lemm, Marius; Schlag, Wilhelm 2 2020 Structure formulas for wave operators under a small scaling invariant condition. Zbl 1428.35254Beceanu, Marius; Schlag, Wilhelm 6 2019 On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling. Zbl 07088060Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 6 2019 Profiles for the radial focusing \(4d\) energy-critical wave equation. Zbl 1404.35294Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 13 2018 Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 1478.47023Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea 8 2018 The Weber equation as a normal form with applications to top of the barrier scattering. Zbl 1414.34067Costin, Rodica D.; Park, Hyejin; Schlag, Wilhelm 2 2018 Long time dynamics for damped Klein-Gordon equations. (Dynamique en temps grand des solutions de l’équation de Klein-Gordon amortie.) Zbl 1392.35041Burq, Nicolas; Raugel, Geneviève; Schlag, Wilhelm 12 2017 Large global solutions for energy supercritical nonlinear wave equations on \(\mathbb{R}^{3+1}\). Zbl 1402.35180Krieger, Joachim; Schlag, Wilhelm 11 2017 Linear stability of the Skyrmion. Zbl 1405.83018Creek, Matthew; Donninger, Roland; Schlag, Wilhelm; Snelson, Stanley 3 2017 Generic and non-generic behavior of solutions to defocusing energy critical wave equation with potential in the radial case. Zbl 1405.35114Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang 3 2017 Characterization of large energy solutions of the equivariant wave map problem. I. Zbl 1315.35130Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 34 2015 Center-stable manifold of the ground state in the energy space for the critical wave equation. Zbl 1315.35133Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 30 2015 Characterization of large energy solutions of the equivariant wave map problem. II. Zbl 1315.35131Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. 26 2015 Channels of energy for the linear radial wave equation. Zbl 1331.35209Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm 17 2015 Stable soliton resolution for exterior wave maps in all equivariance classes. Zbl 1331.35076Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm 13 2015 Full range of blow up exponents for the quintic wave equation in three dimensions. Zbl 1320.35096Krieger, Joachim; Schlag, Wilhelm 30 2014 Relaxation of wave maps exterior to a ball to harmonic maps for all data. Zbl 1288.35356Kenig, Carlos E.; Lawrie, Andrew; Schlag, Wilhelm 21 2014 Threshold phenomenon for the quintic wave equation in three dimensions. Zbl 1297.35139Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 20 2014 Exotic blowup solutions for the \(u^5\) focusing wave equation in \(\mathbb{R}^{3}\). Zbl 1310.35170Donninger, Roland; Huang, Min; Krieger, Joachim; Schlag, Wilhelm 19 2014 Energy partition for the linear radial wave equation. Zbl 1311.35022Côte, Raphaël; Kenig, Carlos E.; Schlag, Wilhelm 16 2014 A course in complex analysis and Riemann surfaces. Zbl 1326.30003Schlag, Wilhelm 7 2014 Semilinear wave equations. Zbl 1373.35181Schlag, Wilhelm 1 2014 The method of concentration compactness and dispersive Hamiltonian evolution equations. Zbl 1319.35112Schlag, W. 1 2014 Classical and multilinear harmonic analysis. Volume I. Zbl 1281.42002Muscalu, Camil; Schlag, Wilhelm 82 2013 Classical and multilinear harmonic analysis. Volume II. Zbl 1282.42001Muscalu, Camil; Schlag, Wilhelm 49 2013 Global dynamics away from the ground state for the energy-critical nonlinear wave equation. Zbl 1307.35170Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 35 2013 Global dynamics of the nonradial energy-critical wave equation above the ground state energy. Zbl 1272.35153Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm 25 2013 Scattering for wave maps exterior to a ball. Zbl 1264.35045Lawrie, A.; Schlag, W. 12 2013 Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Zbl 1321.37023Schlag, Wilhelm 11 2013 Concentration compactness for critical wave maps. Zbl 1387.35006Krieger, Joachim; Schlag, Wilhelm 54 2012 On pointwise decay of linear waves on a Schwarzschild black hole background. Zbl 1242.83054Donninger, Roland; Schlag, Wilhelm; Soffer, Avy 50 2012 Global dynamics above the ground state energy for the cubic NLS equation in 3D. Zbl 1237.35148Nakanishi, K.; Schlag, W. 45 2012 Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption. Zbl 1256.35138Nakanishi, K.; Schlag, W. 21 2012 On the spectral properties of \(L_{\pm }\) in three dimensions. Zbl 1232.35106Costin, Ovidiu; Huang, Min; Schlag, Wilhelm 17 2012 Global dynamics above the ground state energy for the one-dimensional NLKG equation. Zbl 1263.35002Krieger, J.; Nakanishi, K.; Schlag, W. 14 2012 Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation. Zbl 1261.35037Nakanishi, K.; Schlag, W. 9 2012 Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials. Zbl 1258.81038Costin, Ovidiu; Donninger, Roland; Schlag, Wilhelm; Tanveer, Saleh 5 2012 Invariant manifolds and dispersive Hamiltonian evolution equations. Zbl 1235.37002Nakanishi, Kenji; Schlag, Wilhelm 62 2011 A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta. Zbl 1205.83041Donninger, Roland; Schlag, Wilhelm; Soffer, Avy 36 2011 Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation. Zbl 1213.35307Nakanishi, K.; Schlag, W. 29 2011 On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations. Zbl 1268.82013Goldstein, Michael; Schlag, Wilhelm 25 2011 Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation. Zbl 1244.35018Donninger, R.; Schlag, W. 9 2011 Decay for the wave and Schrödinger evolutions on manifolds with conical ends. I. Zbl 1185.35046Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang 22 2010 Decay for the wave and Schrödinger evolutions on manifolds with conical ends. II. Zbl 1187.35032Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang 15 2010 Two Erdős problems on lacunary sequences: chromatic number and Diophantine approximation. Zbl 1215.05074Peres, Yuval; Schlag, Wilhelm 13 2010 Decay estimates for the one-dimensional wave equation with an inverse power potential. Zbl 1241.35018Donninger, Roland; Schlag, Wilhelm 9 2010 Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation. Zbl 1170.35066Krieger, Joachim; Schlag, Wilhelm; Tataru, Daniel 81 2009 Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions. Zbl 1181.35208Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm 41 2009 Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Zbl 1180.35490Schlag, Wilhelm 37 2009 Non-generic blow-up solutions for the critical focusing NLS in 1-D. Zbl 1163.35035Krieger, J.; Schlag, Wilhelm 28 2009 Renormalization and blow up for the critical Yang-Mills problem. Zbl 1183.35203Krieger, J.; Schlag, W.; Tataru, D. 25 2009 On the Hardy-Littlewood majorant problem for random sets. Zbl 1158.42002Mockenhaupt, G.; Schlag, W. 5 2009 Renormalization and blow up for charge one equivariant critical wave maps. Zbl 1139.35021Krieger, J.; Schlag, W.; Tataru, D. 102 2008 Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues. Zbl 1171.82011Goldstein, Michael; Schlag, Wilhelm 43 2008 Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in \(\mathbb R^3\). Zbl 1152.35021Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm 35 2008 Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials. Zbl 1160.35056Costin, Ovidiu; Schlag, Wilhelm; Staubach, Wolfgang; Tanveer, Saleh 6 2008 Dispersive estimates for Schrödinger operators: a survey. Zbl 1143.35001Schlag, W. 79 2007 On the focusing critical semi-linear wave equation. Zbl 1219.35144Krieger, J.; Schlag, W. 42 2007 A remark on Littlewood-Paley theory for the distorted Fourier transform. Zbl 1159.42008Schlag, W. 5 2007 Spectral theory and mathematical physics. A festschrift in honor of Barry Simon’s 60th birthday. Ergodic Schrödinger operators, singular spectrum, orthogonal polynomials, and inverse spectral theory. Based on the SimonFest conference, Pasadena, CA, USA, March 27–31, 2006. Zbl 1110.00015 4 2007 On the formation of gaps in the spectrum of Schrödinger operators with quasi-periodic potentials. Zbl 1208.82027Goldstein, Michael; Schlag, Wilhelm 1 2007 Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension. Zbl 1281.35077Krieger, J.; Schlag, W. 52 2006 Agmon-Kato-Kuroda theorems for a large class of perturbations. Zbl 1092.35073Ionescu, Alexandru D.; Schlag, Wilhelm 31 2006 Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II. Zbl 1146.35324Erdoğan, M. Burak; Schlag, Wilhelm 31 2006 Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation. Zbl 1106.35044Demanet, Laurent; Schlag, Wilhelm 21 2006 Spectral theory and nonlinear partial differential equations: a survey. Zbl 1121.35121Schlag, Wilhelm 20 2006 Dispersive analysis of charge transfer models. Zbl 1130.81053Rodnianski, Igor; Schlag, Wilhelm; Soffer, Avraham 51 2005 Dispersive estimates for Schrödinger operators in dimension two. Zbl 1134.35321Schlag, W. 48 2005 On Schrödinger operators with dynamically defined potentials. Zbl 1143.47301Goldstein, Michael; Schlag, Wilhelm 3 2005 On discrete Schrödinger operators with stochastic potentials. Zbl 1119.39302Schlag, W. 2 2005 Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Zbl 1063.35035Rodnianski, Igor; Schlag, Wilhelm 142 2004 Dispersive estimates for Schrödinger operators in dimensions one and three. Zbl 1086.81077Goldberg, M.; Schlag, W. 84 2004 A limiting absorption principle for the three-dimensional Schrödinger equation with \(L^p\) potentials. Zbl 1069.35063Goldberg, M.; Schlag, W. 34 2004 Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I. Zbl 1080.35102Erdoğan, M. Burak; Schlag, Wilhelm 31 2004 Classical and quantum scattering for a class of long range random potentials. Zbl 1019.81059Rodnianski, Igor; Schlag, Wilhelm 12 2003 On continuum incidence problems related to harmonic analysis. Zbl 1043.42010Schlag, W. 8 2003 Energy growth in Schrödinger’s equation with Markovian forcing. Zbl 1033.81023Erdoğan, M. Burak; Killip, Rowan; Schlag, Wilhelm 3 2003 Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 40 2002 Frequency concentration and location lengths for the Anderson model at small disorders. Zbl 1032.60060Schlag, W.; Shubin, C.; Wolff, Thomas H. 6 2002 Bernoulli convolutions and an intermediate value theorem for entropies of \(k\)-partitions. Zbl 1024.37004Lindenstrauss, Elon; Peres, Yuval; Schlag, Wilhelm 4 2002 Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions. Zbl 0990.39014Goldstein, Michael; Schlag, Wilhelm 97 2001 Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 46 2001 On the integrated density of states for Schrödinger operators on \(\mathbb Z^2\) with quasi periodic potential. Zbl 1031.82023Schlag, Wilhelm 6 2001 Sixty years of Bernoulli convolutions. Zbl 0961.42006Peres, Yuval; Schlag, Wilhelm; Solomyak, Boris 141 2000 Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions. Zbl 0961.42007Peres, Yuval; Schlag, Wilhelm 91 2000 Anderson localization for Schrödinger operators on \(\mathbb{Z}\) with strongly mixing potentials. Zbl 1040.81014Bourgain, Jean; Schlag, Wilhelm 26 2000 \(L^p\to L^q\) estimates for the circular maximal function. Zbl 0981.42012Schlag, Wilhelm 2 2000 On uniformly distributed dilates of finite integer sequences. Zbl 0946.11016Konyagin, S. V.; Ruzsa, I. Z.; Schlag, W. 1 2000 On minima of the absolute value of certain random exponential sums. Zbl 0964.60012Schlag, W. 1 2000 Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle. Zbl 0949.42006Konyagin, S. V.; Schlag, W. 12 1999 A geometric proof of the circular maximal theorem. Zbl 0942.42010Schlag, W. 10 1998 A geometric inequality with applications to the Kakeya problem in three dimensions. Zbl 0939.42012Schlag, W. 5 1998 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 26 1997 A generalization of Bourgain’s circular maximal theorem. Zbl 0867.42010Schlag, W. 24 1997 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,284 Authors 44 Schlag, Wilhelm 31 Merle, Frank 28 Krieger, Joachim 26 Donninger, Roland 24 Damanik, David 24 Martel, Yvan 22 Kenig, Carlos Eduardo 22 Raphael, Pierre 19 Soffer, Avraham 18 Erdoğan, Mehmet Burak 18 Green, William R. 18 Tataru, Daniel 17 Duyckaerts, Thomas 17 Goldberg, Michael Joseph 17 Kopylova, Elena A. 17 Lawrie, Andrew G. W. 15 Cuccagna, Scipio 14 Côte, Raphaël 13 Solomyak, Boris 12 Bourgain, Jean 12 Mizutani, Haruya 12 Nakanishi, Kenji 12 Shmerkin, Pablo S. 12 Yao, Xiaohua 11 D’Ancona, Piero 11 Jitomirskaya, Svetlana Yakovlevna 11 Komech, Alexander Ilich 11 Rodnianski, Igor 11 Zheng, Jiqiang 10 Beceanu, Marius 10 Lee, Sanghyuk 10 Oh, Sung-Jin 10 Szeftel, Jérémie 10 Zhang, Junyong 9 Costin, Ovidiu 9 Fanelli, Luca 9 Glogić, Irfan 9 Jendrej, Jacek 9 Marzuola, Jeremy Louis 9 Orponen, Tuomas 9 Wei, Juncheng 8 Aretakis, Stefanos 8 Klein, Silvius 8 Kowalczyk, Michał 8 Musso, Monica 8 Schörkhuber, Birgit 8 Tao, Kai 8 You, Jiangong 7 Angelopoulos, Yannis 7 Chen, Gong 7 Feng, De-Jun 7 Fillman, Jake 7 Fu, Yan-Song 7 Gajic, Dejan 7 Ibrahim, Slim 7 Maeda, Masaya 7 Muñoz, Claudio 7 Shi, Yunfeng 7 Sigal, Israel Michael 7 Stefanov, Atanas G. 7 Tohaneanu, Mihai 7 Xu, Guixiang 6 Avila, Artur 6 Bjerklöv, Kristian 6 Collot, Charles 6 Cuenin, Jean-Claude 6 Duarte, Pedro 6 Huang, Min 6 Iosevich, Alex 6 Liu, Bochen 6 Mattila, Pertti 6 Simon, Károly 6 Tao, Terence 6 Varjú, Péter Pál 6 Vega, Luis 6 Vougalter, Vitali 6 Wu, Xinfeng 5 Bárány, Balázs 5 Bouclet, Jean-Marc 5 Burq, Nicolas 5 Del Pino, Manuel A. 5 Falconer, Kenneth J. 5 Frank, Rupert L. 5 Ge, Lingrui 5 Germain, Pierre 5 Gorodetskii, Anton Semenovich 5 Han, Rui 5 Hintz, Peter 5 Järvenpää, Esa 5 Järvenpää, Maarit 5 Kesler, Robert M. 5 Krüger, Helge 5 Lau, Kasing 5 Lenzmann, Enno 5 Lindenstrauss, Elon 5 Liu, Wencai 5 Luk, Jonathan 5 Metcalfe, Jason L. 5 Miao, Changxing 5 Muscalu, Camil ...and 1,184 more Authors all top 5 Cited in 242 Serials 109 Communications in Mathematical Physics 79 Journal of Functional Analysis 52 Journal of Differential Equations 47 Advances in Mathematics 45 Transactions of the American Mathematical Society 40 Journal of Mathematical Physics 36 Journal of Mathematical Analysis and Applications 35 Proceedings of the American Mathematical Society 28 Communications in Partial Differential Equations 25 Annales Henri Poincaré 24 Duke Mathematical Journal 23 Inventiones Mathematicae 23 Discrete and Continuous Dynamical Systems 23 Analysis & PDE 20 Journal d’Analyse Mathématique 19 Mathematische Zeitschrift 18 Mathematische Annalen 17 Archive for Rational Mechanics and Analysis 17 Journal of Spectral Theory 16 Ergodic Theory and Dynamical Systems 16 SIAM Journal on Mathematical Analysis 16 Annals of PDE 15 Journal of the European Mathematical Society (JEMS) 15 Séminaire Laurent Schwartz. 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Second Series 2 Manuscripta Mathematica 2 Numerische Mathematik 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University ...and 142 more Serials all top 5 Cited in 57 Fields 810 Partial differential equations (35-XX) 217 Dynamical systems and ergodic theory (37-XX) 212 Harmonic analysis on Euclidean spaces (42-XX) 206 Quantum theory (81-XX) 203 Operator theory (47-XX) 168 Measure and integration (28-XX) 81 Probability theory and stochastic processes (60-XX) 71 Global analysis, analysis on manifolds (58-XX) 70 Statistical mechanics, structure of matter (82-XX) 63 Relativity and gravitational theory (83-XX) 62 Ordinary differential equations (34-XX) 61 Number theory (11-XX) 45 Functional analysis (46-XX) 33 Difference and functional equations (39-XX) 32 Differential geometry (53-XX) 31 Fluid mechanics (76-XX) 27 Numerical analysis (65-XX) 26 Real functions (26-XX) 24 Functions of a complex variable (30-XX) 18 Combinatorics (05-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 14 Optics, electromagnetic theory (78-XX) 13 Topological groups, Lie groups (22-XX) 12 Abstract harmonic analysis (43-XX) 11 Integral transforms, operational calculus (44-XX) 11 Mechanics of particles and systems (70-XX) 10 Convex and discrete geometry (52-XX) 9 Mechanics of deformable solids (74-XX) 9 Systems theory; control (93-XX) 8 Potential theory (31-XX) 7 Special functions (33-XX) 7 Approximations and expansions (41-XX) 6 Algebraic geometry (14-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Statistics (62-XX) 6 Computer science (68-XX) 6 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Astronomy and astrophysics (85-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Integral equations (45-XX) 2 Manifolds and cell complexes (57-XX) 2 Geophysics (86-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 \(K\)-theory (19-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year