## Bourgain, Jean

Compute Distance To:
 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: 16 Publications Co-Authors: 140 Co-Authors with 222 Joint Publications 4,603 Co-Co-Authors
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### 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
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### 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
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### 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)

### Citations contained in zbMATH Open

463 Publications have been cited 11,663 times in 6,955 Documents Cited by Year
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations. Zbl 0787.35097
Bourgain, J.
1993
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098
Bourgain, J.
1993
Another look at Sobolev spaces. Zbl 1103.46310
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
2001
A sum-product estimate in finite fields, and applications. Zbl 1145.11306
Bourgain, Jean; Katz, N.; Tao, Terence C.
2004
Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161
Bourgain, Jean
1998
Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008
Bourgain, J.
1983
Refinements of Strichartz’ inequality and applications to $$2D-NLS$$ with critical nonlinearity. Zbl 0917.35126
Bourgain, Jean
1998
Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178
Bourgain, Jean
1999
Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001
Bourgain, J.
2005
Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126
Bourgain, J.
1994
Sharp thresholds of graph properties, and the $$k$$-SAT problem (with an appendix by Jean Bourgain). Zbl 0932.05084
Friedgut, Ehud
1999
Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein. Zbl 0705.28008
Bourgain, Jean
1989
New volume ratio properties for convex symmetric bodies in $${\mathbb{R}}^ n$$. Zbl 0617.52006
Bourgain, J.; Milman, V. D.
1987
Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131
Bourgain, Jean
1996
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126
Bourgain, Jean
1999
Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037
Bourgain, Jean; Pavlović, Nataša
2008
Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102
Bourgain, Jean
1994
Averages in the plane over convex curves and maximal operators. Zbl 0626.42012
Bourgain, J.
1986
On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005
Bourgain, Jean; Kenig, Carlos E.
2005
Limiting embedding theorems for $$W^{s,p}$$ when $$s\uparrow 1$$ and applications. Zbl 1029.46030
Bourgain, Jean; Brezis, Haïm; Mironescu, Petru
2002
The proof of the $$l^2$$ decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
2015
Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010
Bourgain, Jean; Guth, Larry
2011
On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086
Bourgain, J.
1993
On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035
Bourgain, J.; Goldstein, M.
2000
Uniform expansion bounds for Cayley graphs of $$\text{SL}_2(\mathbb F_p)$$. Zbl 1216.20042
Bourgain, Jean; Gamburd, Alex
2008
On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013
Bourgain, J.
1985
Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083
Bourgain, Jean; Demeter, Ciprian; Guth, Larry
2016
Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014
Bourgain, J.
1991
Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016
Bourgain, Jean; Fremlin, David H.; Talagrand, Michel
1978
Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138
Bourgain, Jean
1997
On the equation $$\text{div }Y=f$$ and application to control of phases. Zbl 1075.35006
Bourgain, Jean; Brezis, Haïm
2003
More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310
Bourgain, J.
2005
Estimates for the number of sums and products and for exponential sums in fields of prime order. Zbl 1093.11057
Bourgain, J.; Glibichuk, A. A.; Konyagin, S. V.
2006
On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013
Bourgain, J.
1991
Lifting in Sobolev spaces. Zbl 0967.46026
Bourgain, Jean; Brézis, Haïm; Mironescu, Petru
2000
Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083
Bourgain, Jean
1995
On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010
Bourgain, J.
1988
Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017
Bourgain, J.; Tzafriri, L.
1987
On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015
Bourgain, J.
1986
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
2017
On triples in arithmetic progression. Zbl 0959.11004
Bourgain, Jean
1999
Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007
Bourgain, Jean
1996
$$H^{1/2}$$ maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
2004
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019
Bourgain, J.; Jitomirskaya, S.
2002
A class of special L//infinity spaces. Zbl 0466.46024
Bourgain, J.; Delbaen, F.
1980
On dentability and the Bishop-Phelps property. Zbl 0365.46021
Bourgain, J.
1977
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
2010
The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013
Bourgain, J.
1986
New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061
Bourgain, Jean; Brezis, Haïm
2007
Approximation of zonoids by zonotopes. Zbl 0682.46008
Bourgain, J.; Lindenstrauss, J.; Milman, V.
1989
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
2013
On the spectral gap for finitely-generated subgroups of $$\text{SU}(2)$$. Zbl 1135.22010
Bourgain, Jean; Gamburd, Alex
2008
On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166
Bourgain, Jean
1996
On wellposedness of the Zakharov system. Zbl 0909.35125
Bourgain, Jean; Colliander, J.
1996
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086
Bourgain, J.; Garaev, M. Z.
2009
Generalization of Selberg’s $$\frac {3}{16}$$ theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
2011
Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096
Bourgain, J.
1993
The influence of variables in product spaces. Zbl 0771.60002
Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan
1992
On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049
Bourgain, J.
2003
New Banach space properties of the disc algebra and $$H^{\infty}$$. Zbl 0574.46039
Bourgain, J.
1984
On the singularity probability of discrete random matrices. Zbl 1186.60003
Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett
2010
On Melnikov’s persistency problem. Zbl 0897.58020
Bourgain, Jean
1997
Limited operators and strict cosingularity. Zbl 0601.47019
Bourgain, Jean; Diestel, Joe
1984
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137
Bourgain, Jean; Wang, W.
1997
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
2011
Double recurrence and almost sure convergence. Zbl 0685.28008
Bourgain, J.
1990
Mordell’s exponential sum estimate revisited. Zbl 1072.11063
Bourgain, J.
2005
On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004
Bourgain, J.
1987
On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026
Bourgain, Jean
1999
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
2015
On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001
Bourgain, J.
1991
Positivity and continuity of the Lyapunov exponent for shifts on $$\mathbb T^d$$ with arbitrary frequency vector and real analytic potential. Zbl 1089.81021
Bourgain, J.
2005
New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013
Bourgain, Jean; Brezis, Haïm
2004
A Szemerédi type theorem for sets of positive density in $$\mathbb R^k$$. Zbl 0609.10043
Bourgain, J.
1986
Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150
Bourgain, Jean
1999
On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061
Bourgain, J.
2005
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
The discretized sum-product and projection theorems. Zbl 1234.11012
Bourgain, Jean
2010
On the pointwise ergodic theorem on $$L^ p$$ for arithmetic sets. Zbl 0642.28011
Bourgain, J.
1988
Nonlinear Schrödinger equations. Zbl 0952.35127
Bourgain, Jean
1999
On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106
Bourgain, Jean
1997
Anderson localization for Schrödinger operators on $$\mathbb{Z}^2$$with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
2002
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
2013
Periodic solutions of nonlinear wave equations. Zbl 0976.35041
Bourgain, Jean
1999
On the structure of the Sobolev space $$H^{1/2}$$ with values into the circle. Zbl 0970.35069
Bourgain, Jean; Brézis, Haïm; Mironescu, Petru
2000
Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019
Bourgain, J.; Jitomirskaya, S.
2002
On $$\Lambda$$ (p)-subsets of squares. Zbl 0692.43005
Bourgain, J.
1989
Sieving and expanders. Zbl 1217.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
2006
Some new estimates on oscillatory integrals. Zbl 0840.42007
Bourgain, Jean
1995
Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). Zbl 0853.35062
Klainerman, Sergiu; Machedon, Matei
1996
Roth’s theorem on progressions revisited. Zbl 1155.11011
Bourgain, Jean
2008
Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043
Bourgain, Jean
2009
On type of metric spaces. Zbl 0617.46024
Bourgain, J.; Milman, V.; Wolfson, H.
1986
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
2012
Bounded orthogonal systems and the $$\Lambda$$ (p)-set problem. Zbl 0674.43004
Bourgain, J.
1989
Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case. Zbl 1301.35145
Bourgain, Jean; Bulut, Aynur
2014
Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011
Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L.
1985
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
2016
Applications of the theory of semi-embeddings to Banach space theory. Zbl 0541.46020
Bourgain, J.; Rosenthal, H. P.
1983
Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Zbl 07471384
Bourgain, Jean; Li, Dong
2021
On discrete Hardy-Littlewood maximal functions over the balls in $$\mathbb{Z}^d$$: dimension-free estimates. Zbl 1446.42026
Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej
2020
Anderson localization for two interacting quasiperiodic particles. Zbl 07040581
Bourgain, Jean; Kachkovskiy, Ilya
2019
Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $$\mathbb{Z}^d$$. Zbl 1431.42033
Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej
2019
Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114
Bourgain, Jean; Li, Dong
2019
Beyond expansion. III: reciprocal geodesics. Zbl 1447.11079
Bourgain, Jean; Kontorovich, Alex
2019
Spectral gaps without the pressure condition. Zbl 1392.37065
Bourgain, Jean; Dyatlov, Semyon
2018
Decoupling for perturbed cones and the mean square of $$|\zeta (\frac{1}{2}+it)|$$. Zbl 07013525
Bourgain, Jean; Watt, Nigel
2018
On dimension-free variational inequalities for averaging operators in $${\mathbb{R}^d}$$. Zbl 1402.42023
Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej
2018
On a homogenization problem. Zbl 1401.35356
Bourgain, J.
2018
2018 Leroy P. Steele Prizes. Zbl 1390.01053
2018
On a paper of Erdős and Szekeres. Zbl 1453.11040
Bourgain, Jean; Chang, Mei-Chu
2018
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
2017
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016
Bourgain, Jean; Demeter, Ciprian
2017
A study guide for the $$l^{2}$$ decoupling theorem. Zbl 1370.42021
Bourgain, Jean; Demeter, Ciprian
2017
Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071
Bourgain, Jean; Dyatlov, Semyon
2017
On the Vinogradov mean value. Zbl 1371.11138
Bourgain, J.
2017
Nonlinear Roth type theorems in finite fields. Zbl 1420.11024
Bourgain, J.; Chang, M.-C.
2017
Decoupling inequalities and some mean-value theorems. Zbl 1380.42008
Bourgain, Jean
2017
Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093
Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming
2017
Sidonicity and variants of Kaczmarz’s problem. (Sidonicité et un problème de Kaczmarz.) Zbl 1388.43008
Bourgain, Jean; Lewko, Mark
2017
Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120
Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév
2017
Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054
Bourgain, Jean; Kontorovich, Alex
2017
Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076
Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter
2017
On random walks in large compact Lie groups. Zbl 1370.60085
Bourgain, Jean
2017
On a problem of Farrell and Vershynin in random matrix theory. Zbl 1366.60008
Bourgain, Jean
2017
Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083
Bourgain, Jean; Demeter, Ciprian; Guth, Larry
2016
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
2016
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
2016
A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024
Bourgain, Jean
2016
Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082
Bourgain, Jean; Demeter, Ciprian
2016
Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
2016
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
2016
Decouplings for surfaces in $$\mathbb{R}^4$$. Zbl 1332.53007
Bourgain, Jean; Demeter, Ciprian
2016
The essential centre of the mod a diagonalization ideal commutant of an $$n$$-tuple of commuting Hermitian operators. Zbl 1375.47011
Bourgain, Jean; Voiculescu, Dan-Virgil
2016
On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012
Bourgain, Jean
2016
On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046
Bourgain, Jean
2016
Affine extractors over large fields with exponential error. Zbl 1419.11132
Bourgain, Jean; Dvir, Zeev; Leeman, Ethan
2016
The proof of the $$l^2$$ decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
2015
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
2015
Strong illposedness of the incompressible Euler equation in integer $$C^m$$ spaces. Zbl 1480.35316
Bourgain, Jean; Li, Dong
2015
A new function space and applications. Zbl 1339.46028
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
2015
A problem on sums of two squares. Zbl 1364.11091
Bombieri, Enrico; Bourgain, Jean
2015
Prescribing the binary digits of primes. II. Zbl 1310.11097
Bourgain, Jean
2015
On the Morse-Sard property and level sets of $$W^{n,1}$$ Sobolev functions on $$\mathbb{R}^n$$. Zbl 1322.46022
Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan
2015
On $$L^p$$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025
Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua
2015
New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013
Bourgain, Jean; Demeter, Ciprian
2015
On Pleijel’s nodal domain theorem. Zbl 1317.35145
Bourgain, Jean
2015
Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007
Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani
2015
The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068
Bourgain, Jean; Kontorovich, Alex
2015
Nodal intersections and $$L^p$$ restriction theorems on the torus. Zbl 1319.58023
Bourgain, Jean; Rudnick, Zeév
2015
Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
2015
A remark on solutions of the Pell equation. Zbl 1372.11039
Bourgain, J.
2015
Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case. Zbl 1301.35145
Bourgain, Jean; Bulut, Aynur
2014
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071
Bourgain, J.; Garaev, M. Z.
2014
On an endpoint Kato-Ponce inequality. Zbl 1340.42021
Bourgain, Jean; Li, Dong
2014
On Zaremba’s conjecture. Zbl 1370.11083
Bourgain, Jean; Kontorovich, Alex
2014
Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case. Zbl 1307.35272
Bourgain, Jean; Bulut, Aynur
2014
Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323
Bourgain, Jean; Bulut, Aynur
2014
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
2014
On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046
Bourgain, Jean; Kontorovich, Alex
2014
An improved estimate in the restricted isometry problem. Zbl 1323.46009
Bourgain, Jean
2014
On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023
Bourgain, Jean
2014
On toral eigenfunctions and the random wave model. Zbl 1305.60013
Bourgain, Jean
2014
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
2014
Additive patterns in multiplicative subgroups. Zbl 1377.11013
Alon, Noga; Bourgain, Jean
2014
Kloosterman sums in residue rings. Zbl 1319.11051
Bourgain, J.; Garaev, M. Z.
2014
Perimeter of sets and BMO-type norms. (Périmètre d’ensembles et normes de type BMO.) Zbl 1316.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio
2014
An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015
Bourgain, J.
2014
Monotone Boolean functions capture their primes. Zbl 1370.11113
Bourgain, Jean
2014
On the control problem for Schrödinger operators on tori. Zbl 1318.35093
Bourgain, Jean
2014
On oscillatory integral operators in higher dimensions. Zbl 1301.42022
Bourgain, Jean
2014
Some Diophantine applications of the theory of group expansion. Zbl 1370.11082
Bourgain, Jean
2014
On eigenvalue spacings for the 1-D Anderson model with singular site distribution. Zbl 1319.35125
Bourgain, Jean
2014
On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians. Zbl 1319.35126
Bourgain, Jean
2014
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
2013
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
2013
On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017
Bourgain, J.
2013
On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017
Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan
2013
Bounds on the density of states for Schrödinger operators. Zbl 1362.35113
Bourgain, Jean; Klein, Abel
2013
Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092
Bourgain, J.
2013
Expansion in SL$$_2(\mathbb R)$$ and monotone expanders. Zbl 1268.05103
Bourgain, Jean; Yehudayoff, Amir
2013
On congruences with products of variables from short intervals and applications. Zbl 1301.11041
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
2013
Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016
Bourgain, Jean; Burq, Nicolas; Zworski, Maciej
2013
Prescribing the binary digits of primes. Zbl 1309.11065
Bourgain, Jean
2013
On the Fourier-Walsh spectrum of the Moebius function. Zbl 1336.11038
Bourgain, J.
2013
Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Zbl 1319.42006
Bourgain, Jean; Demeter, Ciprian
2013
A lower bound for the Lyapounov exponents of the random Schrödinger operator on a strip. Zbl 1432.82016
Bourgain, J.
2013
On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025
Bourgain, J.
2013
On Pleijel’s nodal domain theorem – Retraction notice. Zbl 1464.35160
Bourgain, J.
2013
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
2012
A spectral gap theorem in SU$$(d)$$. Zbl 1254.43010
Bourgain, Jean; Gamburd, Alex
2012
Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047
Bourgain, Jean; Rudnick, Zeév
2012
Expansion in $$\text{SL}_d(\mathbb Z/q\mathbb Z)$$, $$q$$ arbitrary. Zbl 1247.20052
Bourgain, Jean; Varjú, Péter P.
2012
Finitely supported measures on $$\mathrm{SL}_2(\mathbb R)$$ which are absolutely continuous at infinity. Zbl 1272.60004
Bourgain, Jean
2012
On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder. Zbl 1275.82006
Bourgain, J.
2012
Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Zbl 1251.35141
Bourgain, Jean; Bulut, Aynur
2012
Integral Apollonian circle packings and prime curvatures. Zbl 1281.52011
Bourgain, J.
2012
Distribution of elements of cosets of small subgroups and applications. Zbl 1290.11017
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
2012
...and 363 more Documents
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### Cited by 5,368 Authors

 203 Bourgain, Jean 95 Shparlinski, Igor E. 53 Tao, Terence 48 Tzvetkov, Nikolay 44 Oh, Tadahiro 40 Naor, Assaf 34 Iosevich, Alex 34 Shkredov, Il’ya Dmitrievich 32 Brézis, Haïm 32 Damanik, David 31 Geng, Jiansheng 31 Himonas, A. Alexandrou 29 Berti, Massimiliano 29 Kenig, Carlos Eduardo 29 Lee, Sanghyuk 27 Miao, Changxing 25 Mironescu, Petru 25 Nguyen, Hoai-Minh 25 Procesi, Michela 25 Tomczak-Jaegermann, Nicole 24 Guo, Zihua 24 Koldobsky, Alexander L. 24 Van Schaftingen, Jean 23 Guo, Boling 23 Jitomirskaya, Svetlana Yakovlevna 23 Vega, Luis 23 Yuan, Xiaoping 23 Zhang, Bingyu 22 Raphael, Pierre 22 Yan, Wei 22 You, Jiangong 21 Betancor Perez, Jorge Juan 21 Chang, Mei-Chu 21 Paouris, Grigoris 21 Ponce, Gustavo 20 Cui, Shangbin 20 Koh, Doowon 20 Kontorovich, Alex V. 20 Sogge, Christopher D. 19 Colliander, James E. 19 Korolëv, Maksim Aleksandrovich 19 Linares, Felipe 19 Panthee, Mahendra 19 Schlag, Wilhelm 19 Staffilani, Gigliola 19 Veselić, Ivan 19 Vinh, Le Anh 18 Carvajal, Xavier Paredes 18 Demeter, Ciprian 18 Garaev, Moubariz Z. 18 Montalto, Riccardo 17 Giannopoulos, Apostolos A. 17 Li, Yongsheng 17 Wang, Yuzhao 16 Grébert, Benoît 16 Huo, Zhaohui 16 Konyagin, Sergeĭ Vladimirovich 16 Merle, Frank 16 Mirek, Mariusz 16 Pham Van Thang 16 Rudnev, Misha 16 Shakhmurov, Veli B. 16 Squassina, Marco 16 Zheng, Jiqiang 15 Bona, Jerry Lloyd 15 Erdoğan, Mehmet Burak 15 Kim, Sun Kwang 15 Milman, Vitali D. 15 Orlandi, Giandomenico 15 Pajor, Alain 15 Pisier, Gilles 15 Sarnak, Peter Clive 15 Schechtman, Gideon 15 Schlumprecht, Thomas 15 Vargas, Ana M. 15 Wang, Baoxiang 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 Lemańczyk, Mariusz 14 Martel, Yvan 14 Molinet, Luc 14 Rodríguez-Mesa, Lourdes 14 Sanders, Tom 14 Visan, Monica 14 Zvavitch, Artem 13 Argyros, Spiros A. 13 Castro, Alejandro J. 13 Du, Qiang 13 González Ortiz, Manuel 13 Hani, Zaher 13 Herr, Sebastian 13 Isaza, Pedro 13 Killip, Rowan 13 Lacey, Michael T. ...and 5,268 more Authors
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### Cited in 527 Serials

 359 Journal of Functional Analysis 266 Journal of Mathematical Analysis and Applications 245 Proceedings of the American Mathematical Society 230 Israel Journal of Mathematics 188 Journal of Differential Equations 185 Transactions of the American Mathematical Society 170 Communications in Mathematical Physics 157 Advances in Mathematics 129 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 117 Journal d’Analyse Mathématique 99 Comptes Rendus. Mathématique. Académie des Sciences, Paris 95 Duke Mathematical Journal 94 Communications in Partial Differential Equations 81 Journal of Mathematical Physics 77 Journal of the European Mathematical Society (JEMS) 75 Discrete and Continuous Dynamical Systems 74 Mathematische Zeitschrift 72 Mathematische Annalen 71 Geometric and Functional Analysis. GAFA 69 Inventiones Mathematicae 69 Journal of Number Theory 68 Archive for Rational Mechanics and Analysis 61 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 61 The Journal of Geometric Analysis 61 The Journal of Fourier Analysis and Applications 57 Annals of Mathematics. Second Series 54 Ergodic Theory and Dynamical Systems 54 Journal of the American Mathematical Society 51 Revista Matemática Iberoamericana 49 Journal de Mathématiques Pures et Appliquées. Neuvième Série 48 Mathematika 44 Mathematical Proceedings of the Cambridge Philosophical Society 44 Calculus of Variations and Partial Differential Equations 42 Mathematical Notes 42 Acta Mathematica Sinica. English Series 41 SIAM Journal on Mathematical Analysis 40 Monatshefte für Mathematik 40 Communications in Contemporary Mathematics 40 Annales Henri Poincaré 39 Bulletin of the American Mathematical Society. New Series 39 Communications on Pure and Applied Analysis 38 Journal of Dynamics and Differential Equations 36 Discrete & Computational Geometry 35 Proceedings of the Steklov Institute of Mathematics 34 Bulletin of the Australian Mathematical Society 34 Journal of Statistical Physics 33 Positivity 32 Annales de l’Institut Fourier 31 Journal of Evolution Equations 30 Studia Mathematica 30 Archiv der Mathematik 29 Acta Mathematica 28 The Annals of Probability 27 Illinois Journal of Mathematics 26 Acta Arithmetica 26 Indagationes Mathematicae. New Series 26 Journal of Mathematical Sciences (New York) 25 Journal of Spectral Theory 24 Communications on Pure and Applied Mathematics 24 Rocky Mountain Journal of Mathematics 24 Integral Equations and Operator Theory 23 Mathematische Nachrichten 23 Linear Algebra and its Applications 23 International Journal of Number Theory 22 Nonlinearity 22 Journal of Approximation Theory 22 Forum Mathematicum 21 Mathematical Methods in the Applied Sciences 21 Topology and its Applications 21 Physica D 21 Analysis & PDE 21 Science China. Mathematics 20 Arkiv för Matematik 20 Combinatorica 20 Probability Theory and Related Fields 20 Finite Fields and their Applications 19 Frontiers of Mathematics in China 18 Mathematics of Computation 18 European Journal of Combinatorics 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 Journal of Complexity 17 NoDEA. Nonlinear Differential Equations and Applications 17 Journal of Hyperbolic Differential Equations 17 Forum of Mathematics, Sigma 16 Applicable Analysis 16 Journal für die Reine und Angewandte Mathematik 16 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 16 Nonlinear Analysis. Real World Applications 16 Journal of Fixed Point Theory and Applications 15 Compositio Mathematica 15 Glasgow Mathematical Journal 15 SIAM Journal on Computing 15 Potential Analysis 15 St. Petersburg Mathematical Journal 14 Geometriae Dedicata 14 Results in Mathematics 14 Acta Mathematica Hungarica 14 Abstract and Applied Analysis ...and 427 more Serials
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### Cited in 61 Fields

 2,451 Partial differential equations (35-XX) 1,370 Functional analysis (46-XX) 1,026 Number theory (11-XX) 916 Dynamical systems and ergodic theory (37-XX) 911 Harmonic analysis on Euclidean spaces (42-XX) 732 Operator theory (47-XX) 524 Probability theory and stochastic processes (60-XX) 446 Convex and discrete geometry (52-XX) 327 Measure and integration (28-XX) 314 Combinatorics (05-XX) 304 Fluid mechanics (76-XX) 290 Quantum theory (81-XX) 285 Statistical mechanics, structure of matter (82-XX) 244 Global analysis, analysis on manifolds (58-XX) 199 Real functions (26-XX) 166 Calculus of variations and optimal control; optimization (49-XX) 165 Numerical analysis (65-XX) 164 Computer science (68-XX) 152 Functions of a complex variable (30-XX) 139 Abstract harmonic analysis (43-XX) 132 Information and communication theory, circuits (94-XX) 124 Group theory and generalizations (20-XX) 124 Ordinary differential equations (34-XX) 121 Topological groups, Lie groups (22-XX) 120 Linear and multilinear algebra; matrix theory (15-XX) 118 General topology (54-XX) 112 Differential geometry (53-XX) 74 Potential theory (31-XX) 66 Approximations and expansions (41-XX) 64 Geometry (51-XX) 61 Mathematical logic and foundations (03-XX) 60 Mechanics of deformable solids (74-XX) 59 Mechanics of particles and systems (70-XX) 57 Integral equations (45-XX) 55 Difference and functional equations (39-XX) 53 Integral transforms, operational calculus (44-XX) 50 Algebraic geometry (14-XX) 50 Several complex variables and analytic spaces (32-XX) 43 Systems theory; control (93-XX) 38 Statistics (62-XX) 35 Operations research, mathematical programming (90-XX) 30 Optics, electromagnetic theory (78-XX) 22 History and biography (01-XX) 22 Special functions (33-XX) 21 Order, lattices, ordered algebraic structures (06-XX) 20 Biology and other natural sciences (92-XX) 19 Algebraic topology (55-XX) 17 General and overarching topics; collections (00-XX) 17 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) 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) 2 $$K$$-theory (19-XX) 2 Astronomy and astrophysics (85-XX) 1 Category theory; homological algebra (18-XX)

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