Edit Profile (opens in new tab) Bourgain, Jean Compute Distance To: Compute Author ID: bourgain.jean Published as: Bourgain, Jean; Bourgain, J. Further Spellings: Бургейн Жан Homepage: https://www.math.ias.edu/people/faculty/bourgain External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Awards: Fields Medal (1994) · Shaw Prize (2010) · Breakthrough Prize in Mathematics (2017) Documents Indexed: 521 Publications since 1976, including 9 Books 5 Contributions as Editor · 4 Further Contributions Biographic References: 17 Publications Co-Authors: 140 Co-Authors with 222 Joint Publications 4,683 Co-Co-Authors all top 5 Co-Authors 304 single-authored 18 Milman, Vitali D. 15 Brézis, Haïm 13 Konyagin, Sergeĭ Vladimirovich 12 Gamburd, Alexander 11 Demeter, Ciprian 11 Kontorovich, Alex V. 11 Lindenstrauss, Joram 10 Chang, Mei-Chu 9 Shparlinski, Igor E. 8 Rudnick, Zeév 8 Sarnak, Peter Clive 7 Mironescu, Petru 7 Tzafriri, Lior 6 Garaev, Moubariz Z. 5 Alon, Noga M. 5 Gromov, Mikhael Leonidovich 5 Li, Dong 5 Lindenstrauss, Elon 4 Bombieri, Enrico 4 Bulut, Aynur 4 Connes, Alain 4 Mirek, Mariusz 4 Rosenthal, Haskell P. 4 Stein, Elias Menachem 4 Wang, Wei-Min 4 Wróbel, Błażej Jan 3 Berkson, Earl 3 Ford, Kevin B. 3 Goldstein, Michael 3 Guth, Lawrence David 3 Jitomirskaya, Svetlana Yakovlevna 3 Kalai, Gil 3 Schlag, Wilhelm 3 Talagrand, Michel 2 Ambrosio, Luigi 2 Cochrane, Todd 2 Delbaen, Freddy 2 Dilworth, Stephen J. 2 Dirksen, Sjoerd 2 Dyatlov, Semyon 2 Figalli, Alessio 2 Fuchs, Elena D. 2 Furman, Alex 2 Glibichuk, A. A. 2 Kahane, Jean-Pierre 2 Kashin, Boris Sergeevich 2 Katznelson, Yitzhak 2 Kenig, Carlos Eduardo 2 Klainerman, Sergiu 2 Klartag, Bo’az 2 Korobkov, Mikhail V. 2 Kristensen, Jan 2 Kutzarova, Denka N. 2 Mozes, Shahar 2 Nelson, Jelani 2 Nguyen, Hoai-Minh 2 Pajor, Alain 2 Paulhus, Jennifer 2 Pinner, Christopher G. 2 Pisier, Gilles 2 Reinov, Oleg I. 2 Schechtman, Gideon 2 Szarek, Stanislaw Jerzy 2 Varjú, Péter Pál 2 Yehudayoff, Amir 1 Aigner, Martin 1 Aleksandrov, Aleksei B. 1 Argyros, Spiros A. 1 Asmar, Nakhlé Habib 1 Benyamini, Yoav 1 Bergelson, Vitaly 1 Bethuel, Fabrice 1 Bleher, Pavel M. 1 Blomer, Valentin 1 Boshernitzan, Michael D. 1 Bourgain-Chang, Eric 1 Burq, Nicolas 1 Casazza, Peter George 1 Clozel, Laurent 1 Colliander, James E. 1 Davis, William Jay 1 Diestel, Joseph 1 Dvir, Zeev 1 Figiel, Tadeusz 1 Fomin, Sergey Vladimirovich 1 Fremlin, David H. 1 Friedgut, Ehud 1 Furstenberg, Hillel 1 Ghoussoub, Nassif A. 1 Giesecke, M. 1 Gillespie, Thomas Alastair 1 Golse, François 1 Grünbaum, Francisco Alberto 1 Guo, Shaoming 1 Khavin, Viktor Petrovich 1 Johnson, William Buhmann 1 Kachkovskiy, Ilya V. 1 Kahn, Jeff D. 1 Kaloshin, Vadim Yu. 1 Kalton, Nigel John ...and 51 more Co-Authors all top 5 Serials 45 Israel Journal of Mathematics 34 Geometric and Functional Analysis. GAFA 33 Journal d’Analyse Mathématique 30 Comptes Rendus. Mathématique. Académie des Sciences, Paris 24 IMRN. International Mathematics Research Notices 18 Bulletin de la Société Matheḿatique de Belgique. Série B 12 Communications in Mathematical Physics 12 Comptes Rendus de l’Académie des Sciences. Série I 11 Studia Mathematica 11 Inventiones Mathematicae 11 Journal of the European Mathematical Society (JEMS) 9 Journal of Functional Analysis 9 Annals of Mathematics. Second Series 8 Proceedings of the American Mathematical Society 8 Journal of the American Mathematical Society 6 Acta Mathematica 6 Annales de l’Institut Fourier 6 Transactions of the American Mathematical Society 5 Acta Arithmetica 5 Duke Mathematical Journal 4 Journal of Statistical Physics 4 American Journal of Mathematics 4 Fundamenta Mathematicae 4 Journal of the London Mathematical Society. Second Series 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Illinois Journal of Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Nachrichten 3 Notices of the American Mathematical Society 3 Proceedings of the Steklov Institute of Mathematics 2 Communications on Pure and Applied Mathematics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Colloquium Mathematicum 2 Compositio Mathematica 2 Publications Mathématiques 2 Integral Equations and Operator Theory 2 Memoirs of the American Mathematical Society 2 Pacific Journal of Mathematics 2 Ergodic Theory and Dynamical Systems 2 Selecta Mathematica. New Series 2 Discrete and Continuous Dynamical Systems 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Annals of Mathematics Studies 2 Modern Birkhäuser Classics 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Advances in Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Boletim da Sociedade Brasileira de Matemática 1 Bulletin de la Société Mathématique de France 1 Michigan Mathematical Journal 1 Real Analysis Exchange 1 SIAM Journal on Computing 1 Simon Stevin 1 Journal of Operator Theory 1 Chinese Annals of Mathematics. Series B 1 Bulletin of the Iranian Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Discrete & Computational Geometry 1 Revista Matemática Iberoamericana 1 SIAM Journal on Discrete Mathematics 1 Differential and Integral Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Computational Complexity 1 Mathematical Research Letters 1 Sbornik: Mathematics 1 Izvestiya: Mathematics 1 The Journal of Fourier Analysis and Applications 1 Annales Henri Poincaré 1 Moscow Mathematical Journal 1 International Journal of Number Theory 1 Colloquium Publications. American Mathematical Society 1 Lecture Notes in Mathematics 1 Journal of Spectral Theory 1 Discrete Analysis all top 5 Fields 145 Number theory (11-XX) 139 Functional analysis (46-XX) 96 Partial differential equations (35-XX) 88 Harmonic analysis on Euclidean spaces (42-XX) 62 Operator theory (47-XX) 41 Dynamical systems and ergodic theory (37-XX) 38 Probability theory and stochastic processes (60-XX) 35 Statistical mechanics, structure of matter (82-XX) 34 Abstract harmonic analysis (43-XX) 26 Measure and integration (28-XX) 26 Convex and discrete geometry (52-XX) 26 Quantum theory (81-XX) 20 Global analysis, analysis on manifolds (58-XX) 18 Functions of a complex variable (30-XX) 16 Combinatorics (05-XX) 12 General topology (54-XX) 11 Topological groups, Lie groups (22-XX) 9 Computer science (68-XX) 8 History and biography (01-XX) 8 Group theory and generalizations (20-XX) 8 Difference and functional equations (39-XX) 8 Information and communication theory, circuits (94-XX) 6 Mathematical logic and foundations (03-XX) 6 Algebraic geometry (14-XX) 6 Potential theory (31-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Approximations and expansions (41-XX) 5 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Real functions (26-XX) 4 Ordinary differential equations (34-XX) 3 Sequences, series, summability (40-XX) 2 Field theory and polynomials (12-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Fluid mechanics (76-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 466 Publications have been cited 12,049 times in 7,203 Documents Cited by ▼ Year ▼ Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations. Zbl 0787.35097Bourgain, J. 492 1993 Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098Bourgain, J. 388 1993 Another look at Sobolev spaces. Zbl 1103.46310Bourgain, Jean; Brezis, Haim; Mironescu, Petru 215 2001 Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161Bourgain, Jean 175 1998 Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008Bourgain, J. 174 1983 A sum-product estimate in finite fields, and applications. Zbl 1145.11306Bourgain, Jean; Katz, N.; Tao, Terence C. 174 2004 Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126Bourgain, Jean 170 1998 Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178Bourgain, Jean 170 1999 Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001Bourgain, J. 163 2005 Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126Bourgain, J. 157 1994 Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein. Zbl 0705.28008Bourgain, Jean 150 1989 Sharp thresholds of graph properties, and the \(k\)-SAT problem (with an appendix by Jean Bourgain). Zbl 0932.05084Friedgut, Ehud 147 1999 New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006Bourgain, J.; Milman, V. D. 135 1987 Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131Bourgain, Jean 132 1996 Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126Bourgain, Jean 131 1999 Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037Bourgain, Jean; Pavlović, Nataša 128 2008 Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102Bourgain, Jean 126 1994 Averages in the plane over convex curves and maximal operators. Zbl 0626.42012Bourgain, J. 122 1986 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 120 2015 On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005Bourgain, Jean; Kenig, Carlos E. 117 2005 Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030Bourgain, Jean; Brezis, Haïm; Mironescu, Petru 115 2002 Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010Bourgain, Jean; Guth, Larry 108 2011 On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035Bourgain, J.; Goldstein, M. 101 2000 On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013Bourgain, J. 101 1985 Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083Bourgain, Jean; Demeter, Ciprian; Guth, Larry 101 2016 Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014Bourgain, J. 99 1991 Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042Bourgain, Jean; Gamburd, Alex 99 2008 On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086Bourgain, J. 99 1993 On the equation \(\text{div }Y=f\) and application to control of phases. Zbl 1075.35006Bourgain, Jean; Brezis, Haïm 94 2003 Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016Bourgain, Jean; Fremlin, David H.; Talagrand, Michel 92 1978 More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310Bourgain, J. 90 2005 Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138Bourgain, Jean 90 1997 On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013Bourgain, J. 85 1991 Estimates for the number of sums and products and for exponential sums in fields of prime order. Zbl 1093.11057Bourgain, J.; Glibichuk, A. A.; Konyagin, S. V. 85 2006 On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010Bourgain, J. 82 1988 Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017Bourgain, J.; Tzafriri, L. 80 1987 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 79 2017 Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083Bourgain, Jean 79 1995 Lifting in Sobolev spaces. Zbl 0967.46026Bourgain, Jean; Brézis, Haïm; Mironescu, Petru 79 2000 On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015Bourgain, J. 74 1986 Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007Bourgain, Jean 71 1996 On triples in arithmetic progression. Zbl 0959.11004Bourgain, Jean 70 1999 \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030Bourgain, Jean; Brezis, Haim; Mironescu, Petru 69 2004 A class of special L//infinity spaces. Zbl 0466.46024Bourgain, J.; Delbaen, F. 68 1980 Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019Bourgain, J.; Jitomirskaya, S. 68 2002 The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013Bourgain, J. 68 1986 New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061Bourgain, Jean; Brezis, Haïm 66 2007 On dentability and the Bishop-Phelps property. Zbl 0365.46021Bourgain, J. 65 1977 Approximation of zonoids by zonotopes. Zbl 0682.46008Bourgain, J.; Lindenstrauss, J.; Milman, V. 65 1989 Affine linear sieve, expanders, and sum-product. Zbl 1239.11103Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 64 2010 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 61 2013 On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010Bourgain, Jean; Gamburd, Alex 59 2008 On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166Bourgain, Jean 58 1996 On wellposedness of the Zakharov system. Zbl 0909.35125Bourgain, Jean; Colliander, J. 57 1996 On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086Bourgain, J.; Garaev, M. Z. 54 2009 The influence of variables in product spaces. Zbl 0771.60002Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan 53 1992 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 53 2011 Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096Bourgain, J. 53 1993 On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049Bourgain, J. 52 2003 Limited operators and strict cosingularity. Zbl 0601.47019Bourgain, Jean; Diestel, Joe 50 1984 New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039Bourgain, J. 50 1984 Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137Bourgain, Jean; Wang, W. 49 1997 On the singularity probability of discrete random matrices. Zbl 1186.60003Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett 49 2010 On Melnikov’s persistency problem. Zbl 0897.58020Bourgain, Jean 49 1997 Double recurrence and almost sure convergence. Zbl 0685.28008Bourgain, J. 48 1990 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 47 2015 Explicit constructions of RIP matrices and related problems. Zbl 1236.94027Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka 46 2011 On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004Bourgain, J. 43 1987 On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026Bourgain, Jean 43 1999 Mordell’s exponential sum estimate revisited. Zbl 1072.11063Bourgain, J. 43 2005 On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001Bourgain, J. 42 1991 Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential. Zbl 1089.81021Bourgain, J. 42 2005 New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013Bourgain, Jean; Brezis, Haïm 42 2004 A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043Bourgain, J. 41 1986 On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011Bourgain, J. 41 1988 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 40 2013 Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150Bourgain, Jean 40 1999 The discretized sum-product and projection theorems. Zbl 1234.11012Bourgain, Jean 39 2010 On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061Bourgain, J. 39 2005 A note on the Schrödinger maximal function. Zbl 1361.35151Bourgain, J. 39 2016 Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 38 2001 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 37 2013 Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019Bourgain, J.; Jitomirskaya, S. 36 2002 Nonlinear Schrödinger equations. Zbl 0952.35127Bourgain, Jean 36 1999 On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106Bourgain, Jean 36 1997 Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 35 2002 On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005Bourgain, J. 35 1989 Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L. 35 1985 On type of metric spaces. Zbl 0617.46024Bourgain, J.; Milman, V.; Wolfson, H. 34 1986 Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case. Zbl 1301.35145Bourgain, Jean; Bulut, Aynur 34 2014 On the structure of the Sobolev space \(H^{1/2}\) with values into the circle. Zbl 0970.35069Bourgain, Jean; Brézis, Haïm; Mironescu, Petru 34 2000 Periodic solutions of nonlinear wave equations. Zbl 0976.35041Bourgain, Jean 34 1999 Roth’s theorem on progressions revisited. Zbl 1155.11011Bourgain, Jean 33 2008 Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071Bourgain, J.; Garaev, M. Z. 33 2014 Sieving and expanders. Zbl 1217.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 33 2006 On the Cauchy and invariant measure problem for the periodic Zakharov system. Zbl 0821.35120Bourgain, Jean 33 1994 Some new estimates on oscillatory integrals. Zbl 0840.42007Bourgain, Jean 33 1995 Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). Zbl 0853.35062Klainerman, Sergiu; Machedon, Matei 33 1996 On the hidden shifted power problem. Zbl 1311.11111Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 33 2012 Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043Bourgain, Jean 33 2009 Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Zbl 1490.35257Bourgain, Jean; Li, Dong 2 2021 On discrete Hardy-Littlewood maximal functions over the balls in \(\mathbb{Z}^d\): dimension-free estimates. Zbl 1446.42026Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 2 2020 Three applications of the Siegel mass formula. Zbl 1465.11174Bourgain, Jean; Demeter, Ciprian 1 2020 Decouplings for real analytic surfaces of revolution. Zbl 1446.42009Bourgain, Jean; Demeter, Ciprian; Kemp, Dominique 1 2020 Anderson localization for two interacting quasiperiodic particles. Zbl 07040581Bourgain, Jean; Kachkovskiy, Ilya 8 2019 Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in \(\mathbb{Z}^d\). Zbl 1431.42033Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 5 2019 Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114Bourgain, Jean; Li, Dong 4 2019 Beyond expansion. III: reciprocal geodesics. Zbl 1447.11079Bourgain, Jean; Kontorovich, Alex 1 2019 Spectral gaps without the pressure condition. Zbl 1392.37065Bourgain, Jean; Dyatlov, Semyon 19 2018 Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 1486.11117Bourgain, Jean; Watt, Nigel 15 2018 On dimension-free variational inequalities for averaging operators in \({\mathbb{R}^d}\). Zbl 1402.42023Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 9 2018 On a homogenization problem. Zbl 1401.35356Bourgain, J. 5 2018 On a paper of Erdős and Szekeres. Zbl 1453.11040Bourgain, Jean; Chang, Mei-Chu 3 2018 2018 Leroy P. Steele Prizes. Zbl 1390.01053 1 2018 Beyond expansion. IV: Traces of thin semigroups. Zbl 1428.11128Bourgain, Jean; Kontorovich, Alex 1 2018 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 79 2017 Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016Bourgain, Jean; Demeter, Ciprian 24 2017 A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021Bourgain, Jean; Demeter, Ciprian 20 2017 Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071Bourgain, Jean; Dyatlov, Semyon 19 2017 On the Vinogradov mean value. Zbl 1371.11138Bourgain, J. 15 2017 Nonlinear Roth type theorems in finite fields. Zbl 1420.11024Bourgain, J.; Chang, M.-C. 9 2017 Decoupling inequalities and some mean-value theorems. Zbl 1380.42008Bourgain, Jean 7 2017 Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter 6 2017 Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév 5 2017 Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming 5 2017 Sidonicity and variants of Kaczmarz’s problem. (Sidonicité et un problème de Kaczmarz.) Zbl 1388.43008Bourgain, Jean; Lewko, Mark 5 2017 Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054Bourgain, Jean; Kontorovich, Alex 4 2017 On random walks in large compact Lie groups. Zbl 1370.60085Bourgain, Jean 1 2017 On a problem of Farrell and Vershynin in random matrix theory. Zbl 1366.60008Bourgain, Jean 1 2017 Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083Bourgain, Jean; Demeter, Ciprian; Guth, Larry 101 2016 A note on the Schrödinger maximal function. Zbl 1361.35151Bourgain, J. 39 2016 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 17 2016 A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024Bourgain, Jean 13 2016 Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082Bourgain, Jean; Demeter, Ciprian 13 2016 Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter 11 2016 Local statistics of lattice points on the sphere. Zbl 1394.11059Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév 9 2016 Decouplings for surfaces in \(\mathbb{R}^4\). Zbl 1332.53007Bourgain, Jean; Demeter, Ciprian 7 2016 The essential centre of the mod a diagonalization ideal commutant of an \(n\)-tuple of commuting Hermitian operators. Zbl 1375.47011Bourgain, Jean; Voiculescu, Dan-Virgil 5 2016 On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012Bourgain, Jean 2 2016 Affine extractors over large fields with exponential error. Zbl 1419.11132Bourgain, Jean; Dvir, Zeev; Leeman, Ethan 1 2016 On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046Bourgain, Jean 1 2016 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 120 2015 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 47 2015 Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 1480.35316Bourgain, Jean; Li, Dong 28 2015 A new function space and applications. Zbl 1339.46028Bourgain, Jean; Brezis, Haim; Mironescu, Petru 25 2015 Prescribing the binary digits of primes. II. Zbl 1310.11097Bourgain, Jean 20 2015 A problem on sums of two squares. Zbl 1364.11091Bombieri, Enrico; Bourgain, Jean 18 2015 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 18 2015 On the Morse-Sard property and level sets of \(W^{n,1}\) Sobolev functions on \(\mathbb{R}^n\). Zbl 1322.46022Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan 17 2015 New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013Bourgain, Jean; Demeter, Ciprian 12 2015 On Pleijel’s nodal domain theorem. Zbl 1317.35145Bourgain, Jean 10 2015 Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani 9 2015 Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 7 2015 The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068Bourgain, Jean; Kontorovich, Alex 7 2015 Nodal intersections and \(L^p\) restriction theorems on the torus. Zbl 1319.58023Bourgain, Jean; Rudnick, Zeév 5 2015 A remark on solutions of the Pell equation. Zbl 1372.11039Bourgain, J. 3 2015 Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case. Zbl 1301.35145Bourgain, Jean; Bulut, Aynur 34 2014 Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071Bourgain, J.; Garaev, M. Z. 33 2014 On an endpoint Kato-Ponce inequality. Zbl 1340.42021Bourgain, Jean; Li, Dong 31 2014 On Zaremba’s conjecture. Zbl 1370.11083Bourgain, Jean; Kontorovich, Alex 30 2014 Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case. Zbl 1307.35272Bourgain, Jean; Bulut, Aynur 23 2014 Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323Bourgain, Jean; Bulut, Aynur 22 2014 Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. 21 2014 On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046Bourgain, Jean; Kontorovich, Alex 18 2014 On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023Bourgain, Jean 16 2014 An improved estimate in the restricted isometry problem. Zbl 1323.46009Bourgain, Jean 15 2014 On toral eigenfunctions and the random wave model. Zbl 1305.60013Bourgain, Jean 13 2014 Multiplicative congruences with variables from short intervals. Zbl 1385.11002Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 11 2014 Additive patterns in multiplicative subgroups. Zbl 1377.11013Alon, Noga; Bourgain, Jean 9 2014 Kloosterman sums in residue rings. Zbl 1319.11051Bourgain, J.; Garaev, M. Z. 8 2014 Perimeter of sets and BMO-type norms. (Périmètre d’ensembles et normes de type BMO.) Zbl 1316.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio 5 2014 An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015Bourgain, J. 4 2014 Monotone Boolean functions capture their primes. Zbl 1370.11113Bourgain, Jean 3 2014 On the control problem for Schrödinger operators on tori. Zbl 1318.35093Bourgain, Jean 2 2014 On oscillatory integral operators in higher dimensions. Zbl 1301.42022Bourgain, Jean 1 2014 On eigenvalue spacings for the 1-D Anderson model with singular site distribution. Zbl 1319.35125Bourgain, Jean 1 2014 On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians. Zbl 1319.35126Bourgain, Jean 1 2014 Some Diophantine applications of the theory of group expansion. Zbl 1370.11082Bourgain, Jean 1 2014 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 61 2013 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 40 2013 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 37 2013 On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017Bourgain, J. 31 2013 On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan 27 2013 Bounds on the density of states for Schrödinger operators. Zbl 1362.35113Bourgain, Jean; Klein, Abel 24 2013 Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092Bourgain, J. 20 2013 Expansion in SL\(_2(\mathbb R)\) and monotone expanders. Zbl 1268.05103Bourgain, Jean; Yehudayoff, Amir 15 2013 On congruences with products of variables from short intervals and applications. Zbl 1301.11041Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 14 2013 Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016Bourgain, Jean; Burq, Nicolas; Zworski, Maciej 14 2013 Prescribing the binary digits of primes. Zbl 1309.11065Bourgain, Jean 12 2013 On the Fourier-Walsh spectrum of the Moebius function. Zbl 1336.11038Bourgain, J. 6 2013 Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Zbl 1319.42006Bourgain, Jean; Demeter, Ciprian 6 2013 A lower bound for the Lyapounov exponents of the random Schrödinger operator on a strip. Zbl 1432.82016Bourgain, J. 3 2013 On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025Bourgain, J. 2 2013 On Pleijel’s nodal domain theorem – Retraction notice. Zbl 1464.35160Bourgain, J. 2 2013 On the hidden shifted power problem. Zbl 1311.11111Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 33 2012 A spectral gap theorem in SU\((d)\). Zbl 1254.43010Bourgain, Jean; Gamburd, Alex 30 2012 Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047Bourgain, Jean; Rudnick, Zeév 20 2012 Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052Bourgain, Jean; Varjú, Péter P. 18 2012 Finitely supported measures on \(\mathrm{SL}_2(\mathbb R)\) which are absolutely continuous at infinity. Zbl 1272.60004Bourgain, Jean 10 2012 On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder. Zbl 1275.82006Bourgain, J. 9 2012 ...and 366 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,569 Authors 203 Bourgain, Jean 96 Shparlinski, Igor E. 55 Tao, Terence 49 Tzvetkov, Nikolay 46 Oh, Tadahiro 40 Naor, Assaf 34 Iosevich, Alex 34 Shkredov, Il’ya Dmitrievich 33 Damanik, David 33 Himonas, A. Alexandrou 32 Brézis, Haïm 31 Geng, Jiansheng 30 Kenig, Carlos Eduardo 30 Lee, Sanghyuk 29 Berti, Massimiliano 27 Miao, Changxing 26 Nguyen, Hoai-Minh 26 Procesi, Michela 25 Mironescu, Petru 25 Tomczak-Jaegermann, Nicole 25 Van Schaftingen, Jean 25 Yan, Wei 24 Guo, Zihua 24 Koldobsky, Alexander L. 23 Guo, Boling 23 Jitomirskaya, Svetlana Yakovlevna 23 Vega, Luis 23 You, Jiangong 23 Yuan, Xiaoping 23 Zhang, Bingyu 22 Raphael, Pierre 21 Betancor Perez, Jorge Juan 21 Chang, Mei-Chu 21 Paouris, Grigoris 21 Ponce, Gustavo 21 Sogge, Christopher D. 20 Cui, Shangbin 20 Koh, Doowon 20 Kontorovich, Alex V. 20 Staffilani, Gigliola 19 Carvajal, Xavier Paredes 19 Colliander, James E. 19 Korolëv, Maksim Aleksandrovich 19 Li, Yongsheng 19 Linares, Felipe 19 Panthee, Mahendra 19 Schlag, Wilhelm 19 Veselić, Ivan 19 Vinh, Le Anh 18 Demeter, Ciprian 18 Garaev, Moubariz Z. 18 Montalto, Riccardo 18 Rudnev, Misha 17 Giannopoulos, Apostolos A. 17 Mirek, Mariusz 17 Wang, Yuzhao 16 Grébert, Benoît 16 Huo, Zhaohui 16 Konyagin, Sergeĭ Vladimirovich 16 Merle, Frank 16 Pham Van Thang 16 Sarnak, Peter Clive 16 Schlumprecht, Thomas 16 Shakhmurov, Veli B. 16 Squassina, Marco 16 Zheng, Jiqiang 15 Bona, Jerry Lloyd 15 Erdoğan, Mehmet Burak 15 Guth, Lawrence David 15 Kim, Sun Kwang 15 Lemańczyk, Mariusz 15 Milman, Vitali D. 15 Orlandi, Giandomenico 15 Pajor, Alain 15 Pisier, Gilles 15 Schechtman, Gideon 15 Vargas, Ana M. 15 Wang, Baoxiang 15 Xu, Junxiang 14 Acosta Vigil, María Dolores 14 Burq, Nicolas 14 Castillo, Jesús M. F. 14 Du, Qiang 14 Hofmann, Steve 14 Johnson, William Buhmann 14 Kalton, Nigel John 14 Lacey, Michael T. 14 Martel, Yvan 14 Molinet, Luc 14 Rodríguez-Mesa, Lourdes 14 Sanders, Tom 14 Seeger, Andreas 14 Visan, Monica 14 Zvavitch, Artem 13 Argyros, Spiros A. 13 Castro, Alejandro J. 13 González Ortiz, Manuel 13 Hani, Zaher 13 Herr, Sebastian 13 Isaza, Pedro ...and 5,469 more Authors all top 5 Cited in 544 Serials 368 Journal of Functional Analysis 277 Journal of Mathematical Analysis and Applications 249 Proceedings of the American Mathematical Society 232 Israel Journal of Mathematics 192 Transactions of the American Mathematical Society 191 Journal of Differential Equations 174 Communications in Mathematical Physics 162 Advances in Mathematics 131 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 120 Journal d’Analyse Mathématique 100 Comptes Rendus. Mathématique. 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Serie Quarta 17 Chinese Annals of Mathematics. Series B 17 Journal of Complexity 16 Journal für die Reine und Angewandte Mathematik 16 Acta Mathematica Hungarica 16 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 16 Journal of Fixed Point Theory and Applications 16 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 15 Compositio Mathematica 15 Glasgow Mathematical Journal 15 SIAM Journal on Computing 15 Potential Analysis 15 St. Petersburg Mathematical Journal 15 The Ramanujan Journal 14 Geometriae Dedicata ...and 444 more Serials all top 5 Cited in 61 Fields 2,539 Partial differential equations (35-XX) 1,411 Functional analysis (46-XX) 1,070 Number theory (11-XX) 951 Harmonic analysis on Euclidean spaces (42-XX) 948 Dynamical systems and ergodic theory (37-XX) 759 Operator theory (47-XX) 542 Probability theory and stochastic processes (60-XX) 453 Convex and discrete geometry (52-XX) 337 Measure and integration (28-XX) 324 Combinatorics (05-XX) 314 Fluid mechanics (76-XX) 305 Quantum theory (81-XX) 297 Statistical mechanics, structure of matter (82-XX) 252 Global analysis, analysis on manifolds (58-XX) 213 Real functions (26-XX) 175 Numerical analysis (65-XX) 172 Computer science (68-XX) 170 Calculus of variations and optimal control; optimization (49-XX) 161 Functions of a complex variable (30-XX) 142 Abstract harmonic analysis (43-XX) 136 Information and communication theory, circuits (94-XX) 130 Group theory and generalizations (20-XX) 125 Linear and multilinear algebra; matrix theory (15-XX) 125 Topological groups, Lie groups (22-XX) 125 Ordinary differential equations (34-XX) 121 General topology (54-XX) 115 Differential geometry (53-XX) 76 Potential theory (31-XX) 75 Approximations and expansions (41-XX) 66 Geometry (51-XX) 64 Mathematical logic and foundations (03-XX) 62 Mechanics of particles and systems (70-XX) 61 Mechanics of deformable solids (74-XX) 60 Integral equations (45-XX) 56 Difference and functional equations (39-XX) 55 Integral transforms, operational calculus (44-XX) 50 Algebraic geometry (14-XX) 49 Several complex variables and analytic spaces (32-XX) 47 Systems theory; control (93-XX) 40 Statistics (62-XX) 36 Operations research, mathematical programming (90-XX) 30 Optics, electromagnetic theory (78-XX) 23 History and biography (01-XX) 23 Special functions (33-XX) 21 Order, lattices, ordered algebraic structures (06-XX) 21 Biology and other natural sciences (92-XX) 19 General and overarching topics; collections (00-XX) 19 Algebraic topology (55-XX) 18 Sequences, series, summability (40-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Manifolds and cell complexes (57-XX) 12 Geophysics (86-XX) 11 Field theory and polynomials (12-XX) 8 Nonassociative rings and algebras (17-XX) 6 Commutative algebra (13-XX) 6 Relativity and gravitational theory (83-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Associative rings and algebras (16-XX) 3 \(K\)-theory (19-XX) 2 Astronomy and astrophysics (85-XX) 1 Category theory; homological algebra (18-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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