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## Schlag, Wilhelm

Compute Distance To:
 Author ID: schlag.wilhelm Published as: Schlag, Wilhelm; Schlag, W.
 Documents Indexed: 101 Publications since 1991, including 6 Books 2 Contributions as Editor 1 Further Contribution
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#### Co-Authors

 20 single-authored 15 Krieger, Joachim 10 Nakanishi, Kenji 9 Goldstein, Michael 8 Kenig, Carlos Eduardo 7 Donninger, Roland 7 Lawrie, Andrew G. W. 5 Erdoğan, Mehmet Burak 5 Soffer, Avraham 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 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 Voda, Mircea 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 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.
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#### Serials

 9 Communications in Mathematical Physics 7 American Journal of Mathematics 5 Advances in Mathematics 5 IMRN. International Mathematics Research Notices 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 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
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#### Fields

 67 Partial differential equations (35-XX) 28 Quantum theory (81-XX) 22 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 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 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX)

#### Citations contained in zbMATH Open

97 Publications have been cited 2,224 times in 1,190 Documents Cited by Year
Sixty years of Bernoulli convolutions. Zbl 0961.42006
Peres, Yuval; Schlag, Wilhelm; Solomyak, Boris
2000
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Zbl 1063.35035
Rodnianski, Igor; Schlag, Wilhelm
2004
Renormalization and blow up for charge one equivariant critical wave maps. Zbl 1139.35021
Krieger, J.; Schlag, W.; Tataru, D.
2008
Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions. Zbl 0990.39014
Goldstein, Michael; Schlag, Wilhelm
2001
Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions. Zbl 0961.42007
Peres, Yuval; Schlag, Wilhelm
2000
Dispersive estimates for Schrödinger operators in dimensions one and three. Zbl 1086.81077
Goldberg, M.; Schlag, W.
2004
Slow blow-up solutions for the $$H^1(\mathbb R^3)$$ critical focusing semilinear wave equation. Zbl 1170.35066
Krieger, Joachim; Schlag, Wilhelm; Tataru, Daniel
2009
Dispersive estimates for Schrödinger operators: a survey. Zbl 1143.35001
Schlag, W.
2007
Classical and multilinear harmonic analysis. Volume I. Zbl 1281.42002
Muscalu, Camil; Schlag, Wilhelm
2013
Invariant manifolds and dispersive Hamiltonian evolution equations. Zbl 1235.37002
Nakanishi, Kenji; Schlag, Wilhelm
2011
Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension. Zbl 1281.35077
Krieger, J.; Schlag, W.
2006
Concentration compactness for critical wave maps. Zbl 1387.35006
Krieger, Joachim; Schlag, Wilhelm
2012
Dispersive analysis of charge transfer models. Zbl 1130.81053
Rodnianski, Igor; Schlag, Wilhelm; Soffer, Avraham
2005
Dispersive estimates for Schrödinger operators in dimension two. Zbl 1134.35321
Schlag, W.
2005
Global dynamics above the ground state energy for the cubic NLS equation in 3D. Zbl 1237.35148
Nakanishi, K.; Schlag, W.
2012
On the focusing critical semi-linear wave equation. Zbl 1219.35144
Krieger, J.; Schlag, W.
2007
On pointwise decay of linear waves on a Schwarzschild black hole background. Zbl 1242.83054
Donninger, Roland; Schlag, Wilhelm; Soffer, Avy
2012
Classical and multilinear harmonic analysis. Volume II. Zbl 1282.42001
Muscalu, Camil; Schlag, Wilhelm
2013
Anderson localization for Schrödinger operators on $$\mathbb Z$$ with potentials given by the skew-shift. Zbl 0994.82044
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
2001
Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues. Zbl 1171.82011
Goldstein, Michael; Schlag, Wilhelm
2008
Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions. Zbl 1181.35208
Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm
2009
Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Zbl 1180.35490
Schlag, Wilhelm
2009
Anderson localization for Schrödinger operators on $$\mathbb{Z}^2$$with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
2002
A limiting absorption principle for the three-dimensional Schrödinger equation with $$L^p$$ potentials. Zbl 1069.35063
Goldberg, M.; Schlag, W.
2004
Global dynamics away from the ground state for the energy-critical nonlinear wave equation. Zbl 1307.35170
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2013
Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in $$\mathbb R^3$$. Zbl 1152.35021
Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm
2008
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II. Zbl 1146.35324
Erdoğan, M. Burak; Schlag, Wilhelm
2006
A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta. Zbl 1205.83041
Donninger, Roland; Schlag, Wilhelm; Soffer, Avy
2011
Non-generic blow-up solutions for the critical focusing NLS in 1-D. Zbl 1163.35035
Krieger, J.; Schlag, Wilhelm
2009
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I. Zbl 1080.35102
Erdoğan, M. Burak; Schlag, Wilhelm
2004
Agmon-Kato-Kuroda theorems for a large class of perturbations. Zbl 1092.35073
Ionescu, Alexandru D.; Schlag, Wilhelm
2006
Full range of blow up exponents for the quintic wave equation in three dimensions. Zbl 1320.35096
Krieger, Joachim; Schlag, Wilhelm
2014
Center-stable manifold of the ground state in the energy space for the critical wave equation. Zbl 1315.35133
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2015
Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation. Zbl 1213.35307
Nakanishi, K.; Schlag, W.
2011
Schauder and $$L^ p$$ estimates for parabolic systems via Campanato spaces. Zbl 0864.35023
Schlag, Wilhelm
1996
Characterization of large energy solutions of the equivariant wave map problem. I. Zbl 1315.35130
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2015
Anderson localization for Schrödinger operators on $$\mathbb{Z}$$ with strongly mixing potentials. Zbl 1040.81014
Bourgain, Jean; Schlag, Wilhelm
2000
Renormalization and blow up for the critical Yang-Mills problem. Zbl 1183.35203
Krieger, J.; Schlag, W.; Tataru, D.
2009
Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation. Zbl 1106.35044
Demanet, Laurent; Schlag, Wilhelm
2006
Global dynamics of the nonradial energy-critical wave equation above the ground state energy. Zbl 1272.35153
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2013
On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations. Zbl 1268.82013
Goldstein, Michael; Schlag, Wilhelm
2011
Decay for the wave and Schrödinger evolutions on manifolds with conical ends. I. Zbl 1185.35046
Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang
2010
Characterization of large energy solutions of the equivariant wave map problem. II. Zbl 1315.35131
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2015
Relaxation of wave maps exterior to a ball to harmonic maps for all data. Zbl 1288.35356
Kenig, Carlos E.; Lawrie, Andrew; Schlag, Wilhelm
2014
A generalization of Bourgain’s circular maximal theorem. Zbl 0867.42010
Schlag, W.
1997
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption. Zbl 1256.35138
Nakanishi, K.; Schlag, W.
2012
Spectral theory and nonlinear partial differential equations: a survey. Zbl 1121.35121
Schlag, Wilhelm
2006
Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006
Schlag, Wilhelm; Sogge, Christopher D.
1997
Threshold phenomenon for the quintic wave equation in three dimensions. Zbl 1297.35139
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2014
On the spectral properties of $$L_{\pm }$$ in three dimensions. Zbl 1232.35106
Costin, Ovidiu; Huang, Min; Schlag, Wilhelm
2012
Channels of energy for the linear radial wave equation. Zbl 1331.35209
Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm
2015
Exotic blowup solutions for the $$u^5$$ focusing wave equation in $$\mathbb{R}^{3}$$. Zbl 1310.35170
Donninger, Roland; Huang, Min; Krieger, Joachim; Schlag, Wilhelm
2014
Decay for the wave and Schrödinger evolutions on manifolds with conical ends. II. Zbl 1187.35032
Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang
2010
Energy partition for the linear radial wave equation. Zbl 1311.35022
Côte, Raphaël; Kenig, Carlos E.; Schlag, Wilhelm
2014
Classical and quantum scattering for a class of long range random potentials. Zbl 1019.81059
Rodnianski, Igor; Schlag, Wilhelm
2003
Scattering for wave maps exterior to a ball. Zbl 1264.35045
Lawrie, A.; Schlag, W.
2013
Stable soliton resolution for exterior wave maps in all equivariance classes. Zbl 1331.35076
Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm
2015
Two Erdős problems on lacunary sequences: chromatic number and Diophantine approximation. Zbl 1215.05074
Peres, Yuval; Schlag, Wilhelm
2010
Profiles for the radial focusing $$4d$$ energy-critical wave equation. Zbl 1404.35294
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2018
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation. Zbl 1244.35018
Donninger, R.; Schlag, W.
2011
Global dynamics above the ground state energy for the one-dimensional NLKG equation. Zbl 1263.35002
Krieger, J.; Nakanishi, K.; Schlag, W.
2012
Decay estimates for the one-dimensional wave equation with an inverse power potential. Zbl 1241.35018
Donninger, Roland; Schlag, Wilhelm
2010
Large global solutions for energy supercritical nonlinear wave equations on $$\mathbb{R}^{3+1}$$. Zbl 1402.35180
Krieger, Joachim; Schlag, Wilhelm
2017
Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation. Zbl 1261.35037
Nakanishi, K.; Schlag, W.
2012
Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle. Zbl 0949.42006
Konyagin, S. V.; Schlag, W.
1999
Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Zbl 1321.37023
Schlag, Wilhelm
2013
A geometric proof of the circular maximal theorem. Zbl 0942.42010
Schlag, W.
1998
On continuum incidence problems related to harmonic analysis. Zbl 1043.42010
Schlag, W.
2003
Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials. Zbl 1160.35056
Costin, Ovidiu; Schlag, Wilhelm; Staubach, Wolfgang; Tanveer, Saleh
2008
A course in complex analysis and Riemann surfaces. Zbl 1326.30003
Schlag, Wilhelm
2014
Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials. Zbl 1258.81038
Costin, Ovidiu; Donninger, Roland; Schlag, Wilhelm; Tanveer, Saleh
2012
Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 06991338
Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2018
Frequency concentration and location lengths for the Anderson model at small disorders. Zbl 1032.60060
Schlag, W.; Shubin, C.; Wolff, Thomas H.
2002
Long time dynamics for damped Klein-Gordon equations. (Dynamique en temps grand des solutions de l’équation de Klein-Gordon amortie.) Zbl 1392.35041
Burq, Nicolas; Raugel, Geneviève; Schlag, Wilhelm
2017
A remark on Littlewood-Paley theory for the distorted Fourier transform. Zbl 1159.42008
Schlag, W.
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
2007
A geometric inequality with applications to the Kakeya problem in three dimensions. Zbl 0939.42012
Schlag, W.
1998
Structure formulas for wave operators under a small scaling invariant condition. Zbl 1428.35254
Beceanu, Marius; Schlag, Wilhelm
2019
On the Hardy-Littlewood majorant problem for random sets. Zbl 1158.42002
Mockenhaupt, G.; Schlag, W.
2009
On the integrated density of states for Schrödinger operators on $$\mathbb Z^2$$ with quasi periodic potential. Zbl 1031.82023
Schlag, Wilhelm
2001
Energy growth in Schrödinger’s equation with Markovian forcing. Zbl 1033.81023
Erdoğan, M. Burak; Killip, Rowan; Schlag, Wilhelm
2003
Structure formulas for wave operators. Zbl 1445.35234
Beceanu, M.; Schlag, W.
2020
Linear stability of the Skyrmion. Zbl 1405.83018
Creek, Matthew; Donninger, Roland; Schlag, Wilhelm; Snelson, Stanley
2017
On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling. Zbl 07088060
Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2019
$$L^p\to L^q$$ estimates for the circular maximal function. Zbl 0981.42012
Schlag, Wilhelm
2000
Bernoulli convolutions and an intermediate value theorem for entropies of $$k$$-partitions. Zbl 1024.37004
Lindenstrauss, Elon; Peres, Yuval; Schlag, Wilhelm
2002
The Weber equation as a normal form with applications to top of the barrier scattering. Zbl 1414.34067
Costin, Rodica D.; Park, Hyejin; Schlag, Wilhelm
2018
On discrete Schrödinger operators with stochastic potentials. Zbl 1119.39302
Schlag, W.
2005
On Schrödinger operators with dynamically defined potentials. Zbl 1143.47301
Goldstein, Michael; Schlag, Wilhelm
2005
Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base. Zbl 1471.35105
Han, R.; Lemm, M.; Schlag, W.
2020
Generic and non-generic behavior of solutions to defocusing energy critical wave equation with potential in the radial case. Zbl 1405.35114
Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang
2017
On minima of the absolute value of certain random exponential sums. Zbl 0964.60012
Schlag, W.
2000
On uniformly distributed dilates of finite integer sequences. Zbl 0946.11016
Konyagin, S. V.; Ruzsa, I. Z.; Schlag, W.
2000
On the formation of gaps in the spectrum of Schrödinger operators with quasi-periodic potentials. Zbl 1208.82027
Goldstein, Michael; Schlag, Wilhelm
2007
Semilinear wave equations. Zbl 1373.35181
Schlag, Wilhelm
2014
A higher-dimensional Bourgain-Dyatlov fractal uncertainty principle. Zbl 1439.32082
Han, Rui; Schlag, Wilhelm
2020
Global center stable manifold for the defocusing energy critical wave equation with potential. Zbl 1465.35306
Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang
2020
Structure formulas for wave operators. Zbl 1445.35234
Beceanu, M.; Schlag, W.
2020
Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base. Zbl 1471.35105
Han, R.; Lemm, M.; Schlag, W.
2020
A higher-dimensional Bourgain-Dyatlov fractal uncertainty principle. Zbl 1439.32082
Han, Rui; Schlag, Wilhelm
2020
Global center stable manifold for the defocusing energy critical wave equation with potential. Zbl 1465.35306
Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang
2020
Structure formulas for wave operators under a small scaling invariant condition. Zbl 1428.35254
Beceanu, Marius; Schlag, Wilhelm
2019
On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling. Zbl 07088060
Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2019
Profiles for the radial focusing $$4d$$ energy-critical wave equation. Zbl 1404.35294
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2018
Homogeneity of the spectrum for quasi-periodic Schrödinger operators. Zbl 06991338
Damanik, David; Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
2018
The Weber equation as a normal form with applications to top of the barrier scattering. Zbl 1414.34067
Costin, Rodica D.; Park, Hyejin; Schlag, Wilhelm
2018
Large global solutions for energy supercritical nonlinear wave equations on $$\mathbb{R}^{3+1}$$. Zbl 1402.35180
Krieger, Joachim; Schlag, Wilhelm
2017
Long time dynamics for damped Klein-Gordon equations. (Dynamique en temps grand des solutions de l’équation de Klein-Gordon amortie.) Zbl 1392.35041
Burq, Nicolas; Raugel, Geneviève; Schlag, Wilhelm
2017
Linear stability of the Skyrmion. Zbl 1405.83018
Creek, Matthew; Donninger, Roland; Schlag, Wilhelm; Snelson, Stanley
2017
Generic and non-generic behavior of solutions to defocusing energy critical wave equation with potential in the radial case. Zbl 1405.35114
Jia, Hao; Liu, Baoping; Schlag, Wilhelm; Xu, Guixiang
2017
Center-stable manifold of the ground state in the energy space for the critical wave equation. Zbl 1315.35133
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2015
Characterization of large energy solutions of the equivariant wave map problem. I. Zbl 1315.35130
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2015
Characterization of large energy solutions of the equivariant wave map problem. II. Zbl 1315.35131
Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W.
2015
Channels of energy for the linear radial wave equation. Zbl 1331.35209
Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm
2015
Stable soliton resolution for exterior wave maps in all equivariance classes. Zbl 1331.35076
Kenig, Carlos; Lawrie, Andrew; Liu, Baoping; Schlag, Wilhelm
2015
Full range of blow up exponents for the quintic wave equation in three dimensions. Zbl 1320.35096
Krieger, Joachim; Schlag, Wilhelm
2014
Relaxation of wave maps exterior to a ball to harmonic maps for all data. Zbl 1288.35356
Kenig, Carlos E.; Lawrie, Andrew; Schlag, Wilhelm
2014
Threshold phenomenon for the quintic wave equation in three dimensions. Zbl 1297.35139
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2014
Exotic blowup solutions for the $$u^5$$ focusing wave equation in $$\mathbb{R}^{3}$$. Zbl 1310.35170
Donninger, Roland; Huang, Min; Krieger, Joachim; Schlag, Wilhelm
2014
Energy partition for the linear radial wave equation. Zbl 1311.35022
Côte, Raphaël; Kenig, Carlos E.; Schlag, Wilhelm
2014
A course in complex analysis and Riemann surfaces. Zbl 1326.30003
Schlag, Wilhelm
2014
Semilinear wave equations. Zbl 1373.35181
Schlag, Wilhelm
2014
Classical and multilinear harmonic analysis. Volume I. Zbl 1281.42002
Muscalu, Camil; Schlag, Wilhelm
2013
Classical and multilinear harmonic analysis. Volume II. Zbl 1282.42001
Muscalu, Camil; Schlag, Wilhelm
2013
Global dynamics away from the ground state for the energy-critical nonlinear wave equation. Zbl 1307.35170
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2013
Global dynamics of the nonradial energy-critical wave equation above the ground state energy. Zbl 1272.35153
Krieger, Joachim; Nakanishi, Kenji; Schlag, Wilhelm
2013
Scattering for wave maps exterior to a ball. Zbl 1264.35045
Lawrie, A.; Schlag, W.
2013
Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Zbl 1321.37023
Schlag, Wilhelm
2013
Concentration compactness for critical wave maps. Zbl 1387.35006
Krieger, Joachim; Schlag, Wilhelm
2012
Global dynamics above the ground state energy for the cubic NLS equation in 3D. Zbl 1237.35148
Nakanishi, K.; Schlag, W.
2012
On pointwise decay of linear waves on a Schwarzschild black hole background. Zbl 1242.83054
Donninger, Roland; Schlag, Wilhelm; Soffer, Avy
2012
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption. Zbl 1256.35138
Nakanishi, K.; Schlag, W.
2012
On the spectral properties of $$L_{\pm }$$ in three dimensions. Zbl 1232.35106
Costin, Ovidiu; Huang, Min; Schlag, Wilhelm
2012
Global dynamics above the ground state energy for the one-dimensional NLKG equation. Zbl 1263.35002
Krieger, J.; Nakanishi, K.; Schlag, W.
2012
Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation. Zbl 1261.35037
Nakanishi, K.; Schlag, W.
2012
Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials. Zbl 1258.81038
Costin, Ovidiu; Donninger, Roland; Schlag, Wilhelm; Tanveer, Saleh
2012
Invariant manifolds and dispersive Hamiltonian evolution equations. Zbl 1235.37002
Nakanishi, Kenji; Schlag, Wilhelm
2011
A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta. Zbl 1205.83041
Donninger, Roland; Schlag, Wilhelm; Soffer, Avy
2011
Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation. Zbl 1213.35307
Nakanishi, K.; Schlag, W.
2011
On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations. Zbl 1268.82013
Goldstein, Michael; Schlag, Wilhelm
2011
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation. Zbl 1244.35018
Donninger, R.; Schlag, W.
2011
Decay for the wave and Schrödinger evolutions on manifolds with conical ends. I. Zbl 1185.35046
Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang
2010
Decay for the wave and Schrödinger evolutions on manifolds with conical ends. II. Zbl 1187.35032
Schlag, Wilhelm; Soffer, Avy; Staubach, Wolfgang
2010
Two Erdős problems on lacunary sequences: chromatic number and Diophantine approximation. Zbl 1215.05074
Peres, Yuval; Schlag, Wilhelm
2010
Decay estimates for the one-dimensional wave equation with an inverse power potential. Zbl 1241.35018
Donninger, Roland; Schlag, Wilhelm
2010
Slow blow-up solutions for the $$H^1(\mathbb R^3)$$ critical focusing semilinear wave equation. Zbl 1170.35066
Krieger, Joachim; Schlag, Wilhelm; Tataru, Daniel
2009
Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions. Zbl 1181.35208
Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm
2009
Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Zbl 1180.35490
Schlag, Wilhelm
2009
Non-generic blow-up solutions for the critical focusing NLS in 1-D. Zbl 1163.35035
Krieger, J.; Schlag, Wilhelm
2009
Renormalization and blow up for the critical Yang-Mills problem. Zbl 1183.35203
Krieger, J.; Schlag, W.; Tataru, D.
2009
On the Hardy-Littlewood majorant problem for random sets. Zbl 1158.42002
Mockenhaupt, G.; Schlag, W.
2009
Renormalization and blow up for charge one equivariant critical wave maps. Zbl 1139.35021
Krieger, J.; Schlag, W.; Tataru, D.
2008
Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues. Zbl 1171.82011
Goldstein, Michael; Schlag, Wilhelm
2008
Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in $$\mathbb R^3$$. Zbl 1152.35021
Erdoğan, M. Burak; Goldberg, Michael; Schlag, Wilhelm
2008
Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials. Zbl 1160.35056
Costin, Ovidiu; Schlag, Wilhelm; Staubach, Wolfgang; Tanveer, Saleh
2008
Dispersive estimates for Schrödinger operators: a survey. Zbl 1143.35001
Schlag, W.
2007
On the focusing critical semi-linear wave equation. Zbl 1219.35144
Krieger, J.; Schlag, W.
2007
A remark on Littlewood-Paley theory for the distorted Fourier transform. Zbl 1159.42008
Schlag, W.
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
2007
On the formation of gaps in the spectrum of Schrödinger operators with quasi-periodic potentials. Zbl 1208.82027
Goldstein, Michael; Schlag, Wilhelm
2007
Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension. Zbl 1281.35077
Krieger, J.; Schlag, W.
2006
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II. Zbl 1146.35324
Erdoğan, M. Burak; Schlag, Wilhelm
2006
Agmon-Kato-Kuroda theorems for a large class of perturbations. Zbl 1092.35073
Ionescu, Alexandru D.; Schlag, Wilhelm
2006
Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation. Zbl 1106.35044
Demanet, Laurent; Schlag, Wilhelm
2006
Spectral theory and nonlinear partial differential equations: a survey. Zbl 1121.35121
Schlag, Wilhelm
2006
Dispersive analysis of charge transfer models. Zbl 1130.81053
Rodnianski, Igor; Schlag, Wilhelm; Soffer, Avraham
2005
Dispersive estimates for Schrödinger operators in dimension two. Zbl 1134.35321
Schlag, W.
2005
On discrete Schrödinger operators with stochastic potentials. Zbl 1119.39302
Schlag, W.
2005
On Schrödinger operators with dynamically defined potentials. Zbl 1143.47301
Goldstein, Michael; Schlag, Wilhelm
2005
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Zbl 1063.35035
Rodnianski, Igor; Schlag, Wilhelm
2004
Dispersive estimates for Schrödinger operators in dimensions one and three. Zbl 1086.81077
Goldberg, M.; Schlag, W.
2004
A limiting absorption principle for the three-dimensional Schrödinger equation with $$L^p$$ potentials. Zbl 1069.35063
Goldberg, M.; Schlag, W.
2004
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I. Zbl 1080.35102
Erdoğan, M. Burak; Schlag, Wilhelm
2004
Classical and quantum scattering for a class of long range random potentials. Zbl 1019.81059
Rodnianski, Igor; Schlag, Wilhelm
2003
On continuum incidence problems related to harmonic analysis. Zbl 1043.42010
Schlag, W.
2003
Energy growth in Schrödinger’s equation with Markovian forcing. Zbl 1033.81023
Erdoğan, M. Burak; Killip, Rowan; Schlag, Wilhelm
2003
Anderson localization for Schrödinger operators on $$\mathbb{Z}^2$$with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
2002
Frequency concentration and location lengths for the Anderson model at small disorders. Zbl 1032.60060
Schlag, W.; Shubin, C.; Wolff, Thomas H.
2002
Bernoulli convolutions and an intermediate value theorem for entropies of $$k$$-partitions. Zbl 1024.37004
Lindenstrauss, Elon; Peres, Yuval; Schlag, Wilhelm
2002
Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions. Zbl 0990.39014
Goldstein, Michael; Schlag, Wilhelm
2001
Anderson localization for Schrödinger operators on $$\mathbb Z$$ with potentials given by the skew-shift. Zbl 0994.82044
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
2001
On the integrated density of states for Schrödinger operators on $$\mathbb Z^2$$ with quasi periodic potential. Zbl 1031.82023
Schlag, Wilhelm
2001
Sixty years of Bernoulli convolutions. Zbl 0961.42006
Peres, Yuval; Schlag, Wilhelm; Solomyak, Boris
2000
Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions. Zbl 0961.42007
Peres, Yuval; Schlag, Wilhelm
2000
Anderson localization for Schrödinger operators on $$\mathbb{Z}$$ with strongly mixing potentials. Zbl 1040.81014
Bourgain, Jean; Schlag, Wilhelm
2000
$$L^p\to L^q$$ estimates for the circular maximal function. Zbl 0981.42012
Schlag, Wilhelm
2000
On minima of the absolute value of certain random exponential sums. Zbl 0964.60012
Schlag, W.
2000
On uniformly distributed dilates of finite integer sequences. Zbl 0946.11016
Konyagin, S. V.; Ruzsa, I. Z.; Schlag, W.
2000
Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle. Zbl 0949.42006
Konyagin, S. V.; Schlag, W.
1999
A geometric proof of the circular maximal theorem. Zbl 0942.42010
Schlag, W.
1998
A geometric inequality with applications to the Kakeya problem in three dimensions. Zbl 0939.42012
Schlag, W.
1998
A generalization of Bourgain’s circular maximal theorem. Zbl 0867.42010
Schlag, W.
1997
Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006
Schlag, Wilhelm; Sogge, Christopher D.
1997
Schauder and $$L^ p$$ estimates for parabolic systems via Campanato spaces. Zbl 0864.35023
Schlag, Wilhelm
1996
all top 5

#### Cited by 1,116 Authors

 42 Schlag, Wilhelm 28 Merle, Frank 26 Donninger, Roland 25 Krieger, Joachim 21 Damanik, David 21 Martel, Yvan 20 Kenig, Carlos Eduardo 20 Raphael, Pierre 17 Kopylova, Elena A. 17 Soffer, Avraham 16 Erdoğan, Mehmet Burak 16 Goldberg, Michael Joseph 16 Green, William R. 15 Tataru, Daniel 14 Cuccagna, Scipio 14 Duyckaerts, Thomas 13 Côte, Raphaël 13 Lawrie, Andrew G. W. 12 Bourgain, Jean 12 Shmerkin, Pablo S. 11 Komech, Alexander Ilich 11 Mizutani, Haruya 11 Solomyak, Boris 10 D’Ancona, Piero 10 Yao, Xiaohua 9 Beceanu, Marius 9 Jitomirskaya, Svetlana Yakovlevna 9 Nakanishi, Kenji 9 Rodnianski, Igor 9 Wei, Juncheng 8 Costin, Ovidiu 8 Fanelli, Luca 8 Glogić, Irfan 8 Marzuola, Jeremy L. 8 Musso, Monica 8 Oh, Sung-Jin 8 Orponen, Tuomas 8 Schörkhuber, Birgit 8 Szeftel, Jérémie 8 Zheng, Jiqiang 7 Aretakis, Stefanos 7 Feng, De-Jun 7 Jendrej, Jacek 7 Klein, Silvius 7 Lee, Sanghyuk 7 Stefanov, Atanas G. 7 Zhang, Junyong 6 Angelopoulos, Yannis 6 Bjerklöv, Kristian 6 Collot, Charles 6 Gajic, Dejan 6 Huang, Min 6 Ibrahim, Slim 6 Muñoz, Claudio 6 Sigal, Israel Michael 6 Tao, Kai 6 Tao, Terence 6 Tohaneanu, Mihai 6 Varjú, Péter Pál 6 Vega, Luis 6 You, Jiangong 5 Avila Cordeiro de Melo, Artur 5 Chen, Gong 5 Del Pino, Manuel A. 5 Duarte, Pedro 5 Falconer, Kenneth J. 5 Fillman, Jake 5 Iosevich, Alex 5 Järvenpää, Esa 5 Järvenpää, Maarit 5 Kesler, Robert M. 5 Kowalczyk, Michał 5 Krüger, Helge 5 Lau, Kasing 5 Liu, Bochen 5 Mattila, Pertti 5 Metcalfe, Jason L. 5 Pelinovsky, Dmitry Efimovich 5 Perelman, Galina 5 Peres, Yuval 5 Shi, Yunfeng 5 Simon, Károly 5 Tanveer, Saleh 5 Teschl, Gerald 5 Visciglia, Nicola 5 Voda, Mircea 5 Xu, Guixiang 5 Zeng, Chongchun 4 Bahouri, Hajer 4 Balogh, Zoltán M. 4 Bárány, Balázs 4 Barceló, Juan Antonio 4 Bouclet, Jean-Marc 4 Burq, Nicolas 4 Carles, Rémi 4 Chen, Thomas M. 4 Chulaevsky, Victor 4 Ding, Yong 4 Frank, Rupert L. 4 Fu, Yan-Song ...and 1,016 more Authors
all top 5

#### Cited in 216 Serials

 101 Communications in Mathematical Physics 77 Journal of Functional Analysis 45 Journal of Differential Equations 44 Transactions of the American Mathematical Society 38 Advances in Mathematics 36 Journal of Mathematical Physics 33 Journal of Mathematical Analysis and Applications 30 Proceedings of the American Mathematical Society 27 Communications in Partial Differential Equations 23 Duke Mathematical Journal 23 Annales Henri Poincaré 20 Discrete and Continuous Dynamical Systems 17 Mathematische Annalen 16 Archive for Rational Mechanics and Analysis 16 Journal d’Analyse Mathématique 16 Inventiones Mathematicae 14 Ergodic Theory and Dynamical Systems 14 Séminaire Laurent Schwartz. EDP et Applications 13 Journal of the European Mathematical Society (JEMS) 13 Annals of PDE 12 Journal of Statistical Physics 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 SIAM Journal on Mathematical Analysis 12 Journal of Spectral Theory 11 Nonlinearity 11 Mathematische Zeitschrift 11 Journal of the American Mathematical Society 11 Annals of Mathematics. Second Series 10 Memoirs of the American Mathematical Society 10 The Journal of Geometric Analysis 10 Communications on Pure and Applied Analysis 10 Analysis & PDE 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Physica D 9 Revista Matemática Iberoamericana 9 Geometric and Functional Analysis. GAFA 9 The Journal of Fourier Analysis and Applications 9 Mathematical Physics, Analysis and Geometry 8 Communications on Pure and Applied Mathematics 8 Israel Journal of Mathematics 8 Mathematical Proceedings of the Cambridge Philosophical Society 8 Monatshefte für Mathematik 8 Bulletin of the American Mathematical Society. New Series 8 Acta Mathematica Sinica. English Series 8 Journal of Evolution Equations 8 Journal of Fractal Geometry 7 Calculus of Variations and Partial Differential Equations 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Journal of Hyperbolic Differential Equations 6 Journal of Dynamics and Differential Equations 5 Mathematics of Computation 5 Reviews in Mathematical Physics 5 Chaos, Solitons and Fractals 5 Acta Mathematica 5 Illinois Journal of Mathematics 5 Frontiers of Mathematics in China 4 Applicable Analysis 4 Letters in Mathematical Physics 4 Mathematical Methods in the Applied Sciences 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Applied Mathematics and Computation 4 Journal of the Mathematical Society of Japan 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Communications in Contemporary Mathematics 4 Analysis in Theory and Applications 4 Bulletin of Mathematical Sciences 3 Russian Mathematical Surveys 3 Archiv der Mathematik 3 Journal of Number Theory 3 Mathematische Nachrichten 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Chinese Annals of Mathematics. Series B 3 Journal of Scientific Computing 3 Forum Mathematicum 3 St. Petersburg Mathematical Journal 3 Bulletin des Sciences Mathématiques 3 Proceedings of the American Mathematical Society. Series B 2 General Relativity and Gravitation 2 Linear and Multilinear Algebra 2 Ukrainian Mathematical Journal 2 Arkiv för Matematik 2 Annales de l’Institut Fourier 2 The Annals of Probability 2 Collectanea Mathematica 2 Indiana University Mathematics Journal 2 Publications Mathématiques 2 Journal of Computational and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Manuscripta Mathematica 2 Numerische Mathematik 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Acta Mathematica Hungarica 2 Constructive Approximation 2 Random Structures & Algorithms 2 The Annals of Applied Probability 2 Russian Mathematics 2 Potential Analysis 2 Theory of Probability and Mathematical Statistics 2 Journal of Mathematical Sciences (New York) 2 Electronic Journal of Differential Equations (EJDE) ...and 116 more Serials
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#### Cited in 56 Fields

 700 Partial differential equations (35-XX) 188 Dynamical systems and ergodic theory (37-XX) 178 Quantum theory (81-XX) 173 Operator theory (47-XX) 169 Harmonic analysis on Euclidean spaces (42-XX) 145 Measure and integration (28-XX) 65 Probability theory and stochastic processes (60-XX) 64 Global analysis, analysis on manifolds (58-XX) 64 Statistical mechanics, structure of matter (82-XX) 57 Number theory (11-XX) 55 Ordinary differential equations (34-XX) 51 Relativity and gravitational theory (83-XX) 38 Functional analysis (46-XX) 30 Difference and functional equations (39-XX) 27 Differential geometry (53-XX) 25 Numerical analysis (65-XX) 24 Fluid mechanics (76-XX) 21 Real functions (26-XX) 19 Functions of a complex variable (30-XX) 15 Combinatorics (05-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 10 Convex and discrete geometry (52-XX) 10 Optics, electromagnetic theory (78-XX) 9 Abstract harmonic analysis (43-XX) 9 Mechanics of particles and systems (70-XX) 8 Topological groups, Lie groups (22-XX) 8 Integral transforms, operational calculus (44-XX) 8 Systems theory; control (93-XX) 7 Mechanics of deformable solids (74-XX) 6 Algebraic geometry (14-XX) 6 Special functions (33-XX) 6 Approximations and expansions (41-XX) 6 Biology and other natural sciences (92-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Potential theory (31-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 History and biography (01-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Computer science (68-XX) 3 Astronomy and astrophysics (85-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Integral equations (45-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)