Edit Profile 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: 520 Publications since 1976, including 9 Books 5 Contributions as Editor 3 Further Contributions Biographic References: 16 Publications 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 Lindenstrauss, Elon 4 Bombieri, Enrico 4 Bulut, Aynur 4 Connes, Alain 4 Li, Dong 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 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 1 Katz, Nets Hawk ...and 49 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 22 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) 94 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) 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 Fluid mechanics (76-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 461 Publications have been cited 11,210 times in 6,703 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. 458 1993 Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098Bourgain, J. 369 1993 Another look at Sobolev spaces. Zbl 1103.46310Bourgain, Jean; Brezis, Haim; Mironescu, Petru 200 2001 Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126Bourgain, Jean 168 1998 A sum-product estimate in finite fields, and applications. Zbl 1145.11306Bourgain, Jean; Katz, N.; Tao, Terence C. 168 2004 Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008Bourgain, J. 165 1983 Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161Bourgain, Jean 162 1998 Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178Bourgain, Jean 161 1999 Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001Bourgain, J. 151 2005 Sharp thresholds of graph properties, and the \(k\)-SAT problem (with an appendix by Jean Bourgain). Zbl 0932.05084Friedgut, Ehud 143 1999 Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126Bourgain, J. 141 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 140 1989 New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006Bourgain, J.; Milman, V. D. 128 1987 Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126Bourgain, Jean 121 1999 Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131Bourgain, Jean 119 1996 Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037Bourgain, Jean; Pavlović, Nataša 119 2008 Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102Bourgain, Jean 118 1994 Averages in the plane over convex curves and maximal operators. Zbl 0626.42012Bourgain, J. 111 1986 Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030Bourgain, Jean; Brezis, Haïm; Mironescu, Petru 111 2002 On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005Bourgain, Jean; Kenig, Carlos E. 109 2005 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 97 2015 On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086Bourgain, J. 95 1993 Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042Bourgain, Jean; Gamburd, Alex 94 2008 On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013Bourgain, J. 94 1985 On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035Bourgain, J.; Goldstein, M. 93 2000 Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010Bourgain, Jean; Guth, Larry 93 2011 Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014Bourgain, J. 91 1991 Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138Bourgain, Jean 90 1997 Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016Bourgain, Jean; Fremlin, David H.; Talagrand, Michel 89 1978 On the equation \(\text{div }Y=f\) and application to control of phases. Zbl 1075.35006Bourgain, Jean; Brezis, Haïm 89 2003 Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083Bourgain, Jean; Demeter, Ciprian; Guth, Larry 88 2016 More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310Bourgain, J. 85 2005 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. 84 2006 On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013Bourgain, J. 80 1991 Lifting in Sobolev spaces. Zbl 0967.46026Bourgain, Jean; Brézis, Haïm; Mironescu, Petru 78 2000 On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010Bourgain, J. 77 1988 Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083Bourgain, Jean 75 1995 Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017Bourgain, J.; Tzafriri, L. 74 1987 On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015Bourgain, J. 69 1986 \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030Bourgain, Jean; Brezis, Haim; Mironescu, Petru 68 2004 A class of special L//infinity spaces. Zbl 0466.46024Bourgain, J.; Delbaen, F. 66 1980 On triples in arithmetic progression. Zbl 0959.11004Bourgain, Jean 66 1999 Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019Bourgain, J.; Jitomirskaya, S. 64 2002 The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013Bourgain, J. 63 1986 Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007Bourgain, Jean 63 1996 On dentability and the Bishop-Phelps property. Zbl 0365.46021Bourgain, J. 61 1977 New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061Bourgain, Jean; Brezis, Haïm 61 2007 Affine linear sieve, expanders, and sum-product. Zbl 1239.11103Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 61 2010 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 58 2017 Approximation of zonoids by zonotopes. Zbl 0682.46008Bourgain, J.; Lindenstrauss, J.; Milman, V. 58 1989 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 57 2013 On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010Bourgain, Jean; Gamburd, Alex 57 2008 On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166Bourgain, Jean 55 1996 On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086Bourgain, J.; Garaev, M. Z. 53 2009 Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096Bourgain, J. 52 1993 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 52 2011 The influence of variables in product spaces. Zbl 0771.60002Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan 50 1992 On wellposedness of the Zakharov system. Zbl 0909.35125Bourgain, Jean; Colliander, J. 50 1996 New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039Bourgain, J. 49 1984 On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049Bourgain, J. 48 2003 On Melnikov’s persistency problem. Zbl 0897.58020Bourgain, Jean 47 1997 Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137Bourgain, Jean; Wang, W. 46 1997 Limited operators and strict cosingularity. Zbl 0601.47019Bourgain, Jean; Diestel, Joe 45 1984 On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004Bourgain, J. 43 1987 Explicit constructions of RIP matrices and related problems. Zbl 1236.94027Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka 43 2011 On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001Bourgain, J. 42 1991 Mordell’s exponential sum estimate revisited. Zbl 1072.11063Bourgain, J. 42 2005 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. 41 2005 New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013Bourgain, Jean; Brezis, Haïm 41 2004 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 41 2015 Double recurrence and almost sure convergence. Zbl 0685.28008Bourgain, J. 41 1990 On the singularity probability of discrete random matrices. Zbl 1186.60003Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett 40 2010 On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026Bourgain, Jean 39 1999 Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 37 2001 On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011Bourgain, J. 36 1988 A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043Bourgain, J. 35 1986 On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061Bourgain, J. 35 2005 Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150Bourgain, Jean 35 1999 The discretized sum-product and projection theorems. Zbl 1234.11012Bourgain, Jean 34 2010 Nonlinear Schrödinger equations. Zbl 0952.35127Bourgain, Jean 34 1999 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 On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005Bourgain, J. 34 1989 On type of metric spaces. Zbl 0617.46024Bourgain, J.; Milman, V.; Wolfson, H. 33 1986 Sieving and expanders. Zbl 1217.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 33 2006 Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 33 2002 On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106Bourgain, Jean 33 1997 Roth’s theorem on progressions revisited. Zbl 1155.11011Bourgain, Jean 33 2008 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 33 2013 Some new estimates on oscillatory integrals. Zbl 0840.42007Bourgain, Jean 32 1995 Periodic solutions of nonlinear wave equations. Zbl 0976.35041Bourgain, Jean 32 1999 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 32 2013 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 32 2014 Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019Bourgain, J.; Jitomirskaya, S. 31 2002 Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043Bourgain, Jean 31 2009 Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L. 31 1985 A construction of \({\mathcal L}_{\infty}\)-spaces and related Banach spaces. Zbl 0586.46011Bourgain, Jean; Pisier, Gilles 31 1983 Applications of the theory of semi-embeddings to Banach space theory. Zbl 0541.46020Bourgain, J.; Rosenthal, H. P. 30 1983 On the Cauchy and invariant measure problem for the periodic Zakharov system. Zbl 0821.35120Bourgain, Jean 30 1994 Martingales valued in certain subspaces of \(L^1\). Zbl 0445.46015Bourgain, J.; Rosenthal, H. P. 30 1980 Bounded orthogonal systems and the \(\Lambda\) (p)-set problem. Zbl 0674.43004Bourgain, J. 30 1989 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 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 3 2019 Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114Bourgain, Jean; Li, Dong 3 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 14 2018 Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 07013525Bourgain, Jean; Watt, Nigel 13 2018 On dimension-free variational inequalities for averaging operators in \({\mathbb{R}^d}\). Zbl 1402.42023Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 7 2018 On a homogenization problem. Zbl 1401.35356Bourgain, J. 5 2018 2018 Leroy P. Steele Prizes. Zbl 1390.01053 1 2018 On a paper of Erdős and Szekeres. Zbl 1453.11040Bourgain, Jean; Chang, Mei-Chu 1 2018 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 58 2017 Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016Bourgain, Jean; Demeter, Ciprian 20 2017 A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021Bourgain, Jean; Demeter, Ciprian 18 2017 Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071Bourgain, Jean; Dyatlov, Semyon 17 2017 On the Vinogradov mean value. Zbl 1371.11138Bourgain, J. 13 2017 Nonlinear Roth type theorems in finite fields. Zbl 1420.11024Bourgain, J.; Chang, M.-C. 8 2017 Decoupling inequalities and some mean-value theorems. Zbl 1380.42008Bourgain, Jean 7 2017 Sidonicity and variants of Kaczmarz’s problem. (Sidonicité et un problème de Kaczmarz.) Zbl 1388.43008Bourgain, Jean; Lewko, Mark 5 2017 Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming 5 2017 Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter 4 2017 Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév 4 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 88 2016 A note on the Schrödinger maximal function. Zbl 1361.35151Bourgain, J. 29 2016 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 15 2016 Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082Bourgain, Jean; Demeter, Ciprian 11 2016 A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024Bourgain, Jean 9 2016 Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter 9 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 6 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 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 On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012Bourgain, Jean 1 2016 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 97 2015 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 41 2015 Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 06422797Bourgain, Jean; Li, Dong 24 2015 A new function space and applications. Zbl 1339.46028Bourgain, Jean; Brezis, Haim; Mironescu, Petru 22 2015 Prescribing the binary digits of primes. II. Zbl 1310.11097Bourgain, Jean 17 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 16 2015 A problem on sums of two squares. Zbl 1364.11091Bombieri, Enrico; Bourgain, Jean 16 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 13 2015 On Pleijel’s nodal domain theorem. Zbl 1317.35145Bourgain, Jean 10 2015 New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013Bourgain, Jean; Demeter, Ciprian 9 2015 Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani 9 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 Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 5 2015 A remark on solutions of the Pell equation. Zbl 1372.11039Bourgain, J. 2 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 32 2014 Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071Bourgain, J.; Garaev, M. Z. 30 2014 On an endpoint Kato-Ponce inequality. Zbl 1340.42021Bourgain, Jean; Li, Dong 25 2014 On Zaremba’s conjecture. Zbl 1370.11083Bourgain, Jean; Kontorovich, Alex 25 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 21 2014 Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323Bourgain, Jean; Bulut, Aynur 21 2014 Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. 18 2014 On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046Bourgain, Jean; Kontorovich, Alex 15 2014 On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023Bourgain, Jean 14 2014 An improved estimate in the restricted isometry problem. Zbl 1323.46009Bourgain, 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 On toral eigenfunctions and the random wave model. Zbl 1305.60013Bourgain, 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 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 On oscillatory integral operators in higher dimensions. Zbl 1301.42022Bourgain, Jean 1 2014 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 57 2013 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 33 2013 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 32 2013 On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017Bourgain, J. 28 2013 On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan 25 2013 Bounds on the density of states for Schrödinger operators. Zbl 1362.35113Bourgain, Jean; Klein, Abel 22 2013 Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092Bourgain, J. 18 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 12 2013 Prescribing the binary digits of primes. Zbl 1309.11065Bourgain, Jean 9 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 4 2013 A lower bound for the Lyapounov exponents of the random Schrödinger operator on a strip. Zbl 1432.82016Bourgain, J. 3 2013 On Pleijel’s nodal domain theorem – Retraction notice. Zbl 1464.35160Bourgain, J. 2 2013 On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025Bourgain, J. 2 2013 A spectral gap theorem in SU\((d)\). Zbl 1254.43010Bourgain, Jean; Gamburd, Alex 29 2012 On the hidden shifted power problem. Zbl 1311.11111Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 29 2012 Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047Bourgain, Jean; Rudnick, Zeév 19 2012 Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052Bourgain, Jean; Varjú, Péter P. 15 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 Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Zbl 1251.35141Bourgain, Jean; Bulut, Aynur 8 2012 Integral Apollonian circle packings and prime curvatures. Zbl 1281.52011Bourgain, J. 5 2012 Distribution of elements of cosets of small subgroups and applications. Zbl 1290.11017Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 5 2012 A modular Szemerédi-Trotter theorem for hyperbolas. Zbl 1272.11024Bourgain, Jean 4 2012 ...and 361 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,181 Authors 203 Bourgain, Jean 93 Shparlinski, Igor E. 53 Tao, Terence 48 Tzvetkov, Nikolay 43 Oh, Tadahiro 40 Naor, Assaf 34 Iosevich, Alex 33 Shkredov, Il’ya Dmitrievich 32 Brézis, Haïm 32 Damanik, David 31 Himonas, A. Alexandrou 29 Berti, Massimiliano 29 Kenig, Carlos Eduardo 28 Geng, Jiansheng 28 Lee, Sanghyuk 27 Miao, Changxing 25 Mironescu, Petru 25 Procesi, Michela 25 Tomczak-Jaegermann, Nicole 24 Guo, Zihua 24 Nguyen, Hoai-Minh 24 Van Schaftingen, Jean 23 Guo, Boling 23 Zhang, Bingyu 22 Jitomirskaya, Svetlana Yakovlevna 22 Koldobsky, Alexander L. 22 Vega, Luis 22 You, Jiangong 22 Yuan, Xiaoping 21 Chang, Mei-Chu 21 Ponce, Gustavo 21 Raphael, Pierre 20 Betancor Perez, Jorge Juan 20 Cui, Shangbin 20 Koh, Doowon 20 Kontorovich, Alex V. 20 Paouris, Grigoris 19 Colliander, James E. 19 Korolëv, Maksim Aleksandrovich 19 Linares, Felipe 19 Panthee, Mahendra 19 Sogge, Christopher D. 19 Staffilani, Gigliola 19 Veselić, Ivan 19 Yan, Wei 18 Carvajal, Xavier Paredes 18 Demeter, Ciprian 18 Garaev, Moubariz Z. 18 Schlag, Wilhelm 18 Vinh, Le Anh 17 Montalto, Riccardo 17 Wang, Yuzhao 16 Giannopoulos, Apostolos A. 16 Huo, Zhaohui 16 Konyagin, Sergeĭ Vladimirovich 16 Li, Yongsheng 16 Mirek, Mariusz 16 Pham Van Thang 16 Rudnev, Misha 16 Zheng, Jiqiang 15 Bona, Jerry Lloyd 15 Erdoğan, Mehmet Burak 15 Grébert, Benoît 15 Merle, Frank 15 Milman, Vitali D. 15 Orlandi, Giandomenico 15 Pajor, Alain 15 Pisier, Gilles 15 Sarnak, Peter Clive 15 Schechtman, Gideon 15 Schlumprecht, Thomas 15 Shakhmurov, Veli B. 15 Vargas, Ana M. 15 Xu, Junxiang 14 Acosta Vigil, María Dolores 14 Burq, Nicolas 14 Castillo, Jesús M. F. 14 Guth, Lawrence David 14 Hofmann, Steve 14 Johnson, William Buhmann 14 Kalton, Nigel John 14 Kim, Sun Kwang 14 Martel, Yvan 14 Rodríguez-Mesa, Lourdes 14 Sanders, Tom 14 Squassina, Marco 14 Visan, Monica 14 Wang, Baoxiang 13 Argyros, Spiros A. 13 Castro, Alejandro J. 13 González Ortiz, Manuel 13 Hani, Zaher 13 Herr, Sebastian 13 Isaza, Pedro 13 Killip, Rowan 13 Lacey, Michael T. 13 Lee, Han Ju 13 Mendel, Manor 13 Molinet, Luc 13 Ponnusamy, Saminathan ...and 5,081 more Authors all top 5 Cited in 515 Serials 354 Journal of Functional Analysis 264 Journal of Mathematical Analysis and Applications 238 Proceedings of the American Mathematical Society 229 Israel Journal of Mathematics 180 Transactions of the American Mathematical Society 179 Journal of Differential Equations 167 Communications in Mathematical Physics 153 Advances in Mathematics 124 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 114 Journal d’Analyse Mathématique 98 Comptes Rendus. Mathématique. Académie des Sciences, Paris 93 Communications in Partial Differential Equations 90 Duke Mathematical Journal 81 Journal of Mathematical Physics 73 Journal of the European Mathematical Society (JEMS) 70 Mathematische Annalen 70 Discrete and Continuous Dynamical Systems 69 Mathematische Zeitschrift 68 Geometric and Functional Analysis. GAFA 67 Journal of Number Theory 66 Archive for Rational Mechanics and Analysis 63 Inventiones Mathematicae 61 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 58 The Journal of Fourier Analysis and Applications 56 Annals of Mathematics. Second Series 55 The Journal of Geometric Analysis 53 Ergodic Theory and Dynamical Systems 53 Journal of the American Mathematical Society 49 Journal de Mathématiques Pures et Appliquées. Neuvième Série 48 Mathematika 48 Revista Matemática Iberoamericana 44 Mathematical Proceedings of the Cambridge Philosophical Society 43 Calculus of Variations and Partial Differential Equations 42 Mathematical Notes 41 Acta Mathematica Sinica. English Series 40 SIAM Journal on Mathematical Analysis 39 Monatshefte für Mathematik 39 Bulletin of the American Mathematical Society. New Series 38 Communications in Contemporary Mathematics 38 Communications on Pure and Applied Analysis 37 Annales Henri Poincaré 36 Discrete & Computational Geometry 35 Journal of Dynamics and Differential Equations 35 Proceedings of the Steklov Institute of Mathematics 34 Bulletin of the Australian Mathematical Society 33 Journal of Statistical Physics 32 Annales de l’Institut Fourier 31 Positivity 29 Acta Mathematica 28 Studia Mathematica 28 Archiv der Mathematik 27 Illinois Journal of Mathematics 26 The Annals of Probability 26 Journal of Mathematical Sciences (New York) 26 Journal of Evolution Equations 24 Communications on Pure and Applied Mathematics 24 Acta Arithmetica 24 Integral Equations and Operator Theory 24 Indagationes Mathematicae. New Series 23 Rocky Mountain Journal of Mathematics 23 Mathematische Nachrichten 23 Linear Algebra and its Applications 22 Nonlinearity 22 Journal of Approximation Theory 22 International Journal of Number Theory 22 Journal of Spectral Theory 21 Mathematical Methods in the Applied Sciences 21 Topology and its Applications 21 Analysis & PDE 20 Arkiv för Matematik 20 Combinatorica 20 Physica D 20 Probability Theory and Related Fields 20 Science China. Mathematics 19 Finite Fields and their Applications 19 Frontiers of Mathematics in China 18 European Journal of Combinatorics 18 Forum Mathematicum 17 Annali di Matematica Pura ed Applicata. Serie Quarta 17 Proceedings of the Edinburgh Mathematical Society. Series II 17 Chinese Annals of Mathematics. Series B 17 NoDEA. Nonlinear Differential Equations and Applications 17 Forum of Mathematics, Sigma 16 Mathematics of Computation 16 Journal für die Reine und Angewandte Mathematik 16 Nonlinear Analysis. Real World Applications 16 Journal of Hyperbolic Differential Equations 15 Applicable Analysis 15 Compositio Mathematica 15 Glasgow Mathematical Journal 15 Journal of Complexity 15 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 15 Potential Analysis 15 St. Petersburg Mathematical Journal 15 Journal of Fixed Point Theory and Applications 14 Geometriae Dedicata 14 Acta Mathematica Hungarica 14 Abstract and Applied Analysis 13 Results in Mathematics 13 SIAM Journal on Computing ...and 415 more Serials all top 5 Cited in 61 Fields 2,355 Partial differential equations (35-XX) 1,327 Functional analysis (46-XX) 979 Number theory (11-XX) 878 Dynamical systems and ergodic theory (37-XX) 869 Harmonic analysis on Euclidean spaces (42-XX) 709 Operator theory (47-XX) 499 Probability theory and stochastic processes (60-XX) 433 Convex and discrete geometry (52-XX) 321 Measure and integration (28-XX) 302 Combinatorics (05-XX) 290 Fluid mechanics (76-XX) 282 Quantum theory (81-XX) 274 Statistical mechanics, structure of matter (82-XX) 234 Global analysis, analysis on manifolds (58-XX) 193 Real functions (26-XX) 167 Calculus of variations and optimal control; optimization (49-XX) 158 Numerical analysis (65-XX) 157 Computer science (68-XX) 148 Functions of a complex variable (30-XX) 133 Abstract harmonic analysis (43-XX) 126 Information and communication theory, circuits (94-XX) 120 Topological groups, Lie groups (22-XX) 118 Group theory and generalizations (20-XX) 118 Ordinary differential equations (34-XX) 115 General topology (54-XX) 111 Linear and multilinear algebra; matrix theory (15-XX) 105 Differential geometry (53-XX) 72 Potential theory (31-XX) 64 Approximations and expansions (41-XX) 60 Mathematical logic and foundations (03-XX) 59 Mechanics of particles and systems (70-XX) 58 Mechanics of deformable solids (74-XX) 57 Geometry (51-XX) 56 Integral equations (45-XX) 54 Difference and functional equations (39-XX) 52 Integral transforms, operational calculus (44-XX) 49 Algebraic geometry (14-XX) 47 Several complex variables and analytic spaces (32-XX) 41 Systems theory; control (93-XX) 33 Statistics (62-XX) 32 Operations research, mathematical programming (90-XX) 29 Optics, electromagnetic theory (78-XX) 22 Biology and other natural sciences (92-XX) 21 History and biography (01-XX) 21 Order, lattices, ordered algebraic structures (06-XX) 21 Special functions (33-XX) 19 Algebraic topology (55-XX) 18 General and overarching topics; collections (00-XX) 18 Sequences, series, summability (40-XX) 14 Manifolds and cell complexes (57-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Field theory and polynomials (12-XX) 11 Geophysics (86-XX) 8 Nonassociative rings and algebras (17-XX) 7 Relativity and gravitational theory (83-XX) 6 Commutative algebra (13-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Associative rings and algebras (16-XX) 3 Category theory; homological algebra (18-XX) 2 \(K\)-theory (19-XX) 2 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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