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Bourgain, Jean

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Author ID: bourgain.jean Recent zbMATH articles by "Bourgain, Jean"
Published as: Bourgain, J.; Bourgain, Jean
Homepage: https://www.math.ias.edu/people/faculty/bourgain
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor
Awards: Fields Medal (1994) · Shaw Prize (2010) · Breakthrough Prize in Mathematics (2017)
Documents Indexed: 524 Publications since 1976, including 14 Books
Biographic References: 13 Publications
all top 5

Co-Authors

305 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 Rosenthal, Haskell P.
4 Wang, Wei-Min
3 Berkson, Earl
3 Ford, Kevin B.
3 Goldstein, Michael
3 Guth, Lawrence David
3 Jitomirskaya, Svetlana Ya.
3 Kalai, Gil
3 Mirek, Mariusz
3 Schlag, Wilhelm
3 Stein, Elias Menachem
3 Talagrand, Michel
3 Wróbel, Błażej Jan
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 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 Yehudayoff, Amir
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 Fremlin, David H.
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
1 Katznelson, Yitzhak
1 Kemp, Dominique
1 Kesten, Harry
1 Klainerman, Sergiu
1 Klein, Abel
1 Kostyukovsky, Sergey
...and 42 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
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
7 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 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 Notices of the American Mathematical Society
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)
86 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)
33 Abstract harmonic analysis (43-XX)
26 Measure and integration (28-XX)
26 Convex and discrete geometry (52-XX)
26 Quantum theory (81-XX)
19 Global analysis, analysis on manifolds (58-XX)
18 Functions of a complex variable (30-XX)
15 Combinatorics (05-XX)
12 General topology (54-XX)
11 Topological groups, Lie groups (22-XX)
9 Computer science (68-XX)
8 Group theory and generalizations (20-XX)
8 Difference and functional equations (39-XX)
8 Information and communication theory, circuits (94-XX)
7 History and biography (01-XX)
7 Potential theory (31-XX)
6 Mathematical logic and foundations (03-XX)
6 Algebraic geometry (14-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

Citations contained in zbMATH Open

455 Publications have been cited 10,309 times in 6,233 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.
432
1993
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098
Bourgain, J.
348
1993
Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178
Bourgain, Jean
184
1999
Another look at Sobolev spaces. Zbl 1103.46310
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
177
2001
A sum-product estimate in finite fields, and applications. Zbl 1145.11306
Bourgain, Jean; Katz, N.; Tao, Terence C.
157
2004
Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001
Bourgain, J.
155
2005
Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126
Bourgain, Jean
155
1998
Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008
Bourgain, J.
155
1983
Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161
Bourgain, Jean
149
1998
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126
Bourgain, Jean
128
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
127
1989
Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126
Bourgain, J.
125
1994
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006
Bourgain, J.; Milman, V. D.
122
1987
Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102
Bourgain, Jean
113
1994
Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037
Bourgain, Jean; Pavlović, Nataša
104
2008
Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030
Bourgain, Jean; Brezis, Haïm; Mironescu, Petru
103
2002
Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131
Bourgain, Jean
102
1996
Averages in the plane over convex curves and maximal operators. Zbl 0626.42012
Bourgain, J.
96
1986
On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005
Bourgain, Jean; Kenig, Carlos E.
93
2005
On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086
Bourgain, J.
91
1993
On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013
Bourgain, J.
91
1985
Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042
Bourgain, Jean; Gamburd, Alex
90
2008
On the equation \(\text{div }Y=f\) and application to control of phases. Zbl 1075.35006
Bourgain, Jean; Brezis, Haïm
90
2003
Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138
Bourgain, Jean
87
1997
Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016
Bourgain, Jean; Fremlin, David H.; Talagrand, Michel
87
1978
On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035
Bourgain, J.; Goldstein, M.
85
2000
Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014
Bourgain, J.
80
1991
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.
79
2006
Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010
Bourgain, Jean; Guth, Larry
78
2011
On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013
Bourgain, J.
78
1991
More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310
Bourgain, J.
77
2005
The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
75
2015
Lifting in Sobolev spaces. Zbl 0967.46026
Bourgain, Jean; Brézis, Haïm; Mironescu, Petru
73
2000
Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083
Bourgain, Jean
69
1995
On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010
Bourgain, J.
68
1988
Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017
Bourgain, J.; Tzafriri, L.
68
1987
\(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
66
2004
A class of special L//infinity spaces. Zbl 0466.46024
Bourgain, J.; Delbaen, F.
65
1980
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
63
2016
On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015
Bourgain, J.
62
1986
On triples in arithmetic progression. Zbl 0959.11004
Bourgain, Jean
60
1999
On dentability and the Bishop-Phelps property. Zbl 0365.46021
Bourgain, J.
60
1977
Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007
Bourgain, Jean
59
1996
The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013
Bourgain, J.
59
1986
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019
Bourgain, J.; Jitomirskaya, S.
58
2002
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
56
2010
New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061
Bourgain, Jean; Brezis, Haïm
56
2007
On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010
Bourgain, Jean; Gamburd, Alex
52
2008
Approximation of zonoids by zonotopes. Zbl 0682.46008
Bourgain, J.; Lindenstrauss, J.; Milman, V.
51
1989
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
50
2013
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086
Bourgain, J.; Garaev, M. Z.
50
2009
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
49
2011
Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096
Bourgain, J.
49
1993
New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039
Bourgain, J.
47
1984
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
46
2017
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137
Bourgain, Jean; Wang, W.
46
1997
The influence of variables in product spaces. Zbl 0771.60002
Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan
46
1992
On wellposedness of the Zakharov system. Zbl 0909.35125
Bourgain, Jean; Colliander, J.
45
1996
On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166
Bourgain, Jean
45
1996
On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049
Bourgain, J.
44
2003
Limited operators and strict cosingularity. Zbl 0601.47019
Bourgain, Jean; Diestel, Joe
43
1984
On Melnikov’s persistency problem. Zbl 0897.58020
Bourgain, Jean
42
1997
On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004
Bourgain, J.
42
1987
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
41
2011
Mordell’s exponential sum estimate revisited. Zbl 1072.11063
Bourgain, J.
41
2005
On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001
Bourgain, J.
41
1991
Double recurrence and almost sure convergence. Zbl 0685.28008
Bourgain, J.
39
1990
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.
37
2005
New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013
Bourgain, Jean; Brezis, Haïm
37
2004
On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026
Bourgain, Jean
37
1999
Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
36
2001
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
35
2015
Nonlinear Schrödinger equations. Zbl 0952.35127
Bourgain, Jean
35
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
34
2000
On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061
Bourgain, J.
33
2005
Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150
Bourgain, Jean
33
1999
On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106
Bourgain, Jean
33
1997
Sieving and expanders. Zbl 1217.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
32
2006
Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
32
2002
A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043
Bourgain, J.
32
1986
Vector-valued singular integrals and the \(H^ 1\)-BMO duality. Zbl 0602.42015
Bourgain, Jean
32
1986
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
31
2013
Roth’s theorem on progressions revisited. Zbl 1155.11011
Bourgain, Jean
31
2008
On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005
Bourgain, J.
31
1989
On type of metric spaces. Zbl 0617.46024
Bourgain, J.; Milman, V.; Wolfson, H.
31
1986
A construction of \({\mathcal L}_{\infty}\)-spaces and related Banach spaces. Zbl 0586.46011
Bourgain, Jean; Pisier, Gilles
31
1983
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
30
2013
On the singularity probability of discrete random matrices. Zbl 1186.60003
Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett
30
2010
Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043
Bourgain, Jean
30
2009
Periodic solutions of nonlinear wave equations. Zbl 0976.35041
Bourgain, Jean
30
1999
On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011
Bourgain, J.
30
1988
Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011
Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L.
30
1985
Applications of the theory of semi-embeddings to Banach space theory. Zbl 0541.46020
Bourgain, J.; Rosenthal, H. P.
30
1983
Martingales valued in certain subspaces of \(L^1\). Zbl 0445.46015
Bourgain, J.; Rosenthal, H. P.
30
1980
On the distribution of free path lengths for the periodic Lorentz gas. Zbl 0910.60082
Bourgain, Jean; Golse, François; Wennberg, Bernt
29
1998
On a problem of Kadison and Singer. Zbl 0729.47028
Bourgain, J.; Tzafriri, L.
29
1991
Bounded orthogonal systems and the \(\Lambda\) (p)-set problem. Zbl 0674.43004
Bourgain, J.
29
1989
The discretized sum-product and projection theorems. Zbl 1234.11012
Bourgain, Jean
28
2010
Estimates on exponential sums related to the Diffie-Hellman distributions. Zbl 1102.11041
Bourgain, J.
28
2005
Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019
Bourgain, J.; Jitomirskaya, S.
28
2002
Anderson localization for two interacting quasiperiodic particles. Zbl 07040581
Bourgain, Jean; Kachkovskiy, Ilya
6
2019
Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114
Bourgain, Jean; Li, Dong
2
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
2
2019
Spectral gaps without the pressure condition. Zbl 1392.37065
Bourgain, Jean; Dyatlov, Semyon
10
2018
Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 07013525
Bourgain, Jean; Watt, Nigel
6
2018
On a homogenization problem. Zbl 1401.35356
Bourgain, J.
5
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
4
2018
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
46
2017
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016
Bourgain, Jean; Demeter, Ciprian
16
2017
Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071
Bourgain, Jean; Dyatlov, Semyon
11
2017
A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021
Bourgain, Jean; Demeter, Ciprian
9
2017
On the Vinogradov mean value. Zbl 1371.11138
Bourgain, J.
8
2017
Decoupling inequalities and some mean-value theorems. Zbl 1380.42008
Bourgain, Jean
6
2017
Nonlinear Roth type theorems in finite fields. Zbl 1420.11024
Bourgain, J.; Chang, M.-C.
6
2017
Sidonicity and variants of Kaczmarz’s problem. Zbl 1388.43008
Bourgain, Jean; Lewko, Mark
5
2017
Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 07006293
Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter
4
2017
Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120
Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév
4
2017
Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093
Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming
4
2017
Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054
Bourgain, Jean; Kontorovich, Alex
3
2017
On a problem of Farrell and Vershynin in random matrix theory. Zbl 1366.60008
Bourgain, Jean
1
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
63
2016
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
22
2016
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
15
2016
Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082
Bourgain, Jean; Demeter, Ciprian
10
2016
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
9
2016
Markoff triples and strong approximation. Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
8
2016
A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024
Bourgain, Jean
6
2016
Decouplings for surfaces in \(\mathbb{R}^4\). Zbl 1332.53007
Bourgain, Jean; Demeter, Ciprian
6
2016
The essential centre of the mod a diagonalization ideal commutant of an \(n\)-tuple of commuting Hermitian operators. Zbl 1375.47011
Bourgain, Jean; Voiculescu, Dan-Virgil
5
2016
Affine extractors over large fields with exponential error. Zbl 1419.11132
Bourgain, Jean; Dvir, Zeev; Leeman, Ethan
1
2016
On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012
Bourgain, Jean
1
2016
On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046
Bourgain, Jean
1
2016
The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
75
2015
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
35
2015
A new function space and applications. Zbl 1339.46028
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
21
2015
Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 06422797
Bourgain, Jean; Li, Dong
21
2015
Prescribing the binary digits of primes. II. Zbl 1310.11097
Bourgain, Jean
15
2015
A problem on sums of two squares. Zbl 1364.11091
Bombieri, Enrico; Bourgain, Jean
13
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
13
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
10
2015
New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013
Bourgain, Jean; Demeter, Ciprian
8
2015
On Pleijel’s nodal domain theorem. Zbl 1317.35145
Bourgain, Jean
8
2015
The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068
Bourgain, Jean; Kontorovich, Alex
6
2015
Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007
Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani
5
2015
Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
5
2015
Nodal intersections and \(L^p\) restriction theorems on the torus. Zbl 1319.58023
Bourgain, Jean; Rudnick, Zeév
5
2015
A remark on solutions of the Pell equation. Zbl 1372.11039
Bourgain, J.
2
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
27
2014
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071
Bourgain, J.; Garaev, M. Z.
25
2014
On Zaremba’s conjecture. Zbl 1370.11083
Bourgain, Jean; Kontorovich, Alex
22
2014
On an endpoint Kato-Ponce inequality. Zbl 1340.42021
Bourgain, Jean; Li, Dong
19
2014
Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323
Bourgain, Jean; Bulut, Aynur
17
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
16
2014
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
15
2014
On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046
Bourgain, Jean; Kontorovich, Alex
13
2014
An improved estimate in the restricted isometry problem. Zbl 1323.46009
Bourgain, Jean
11
2014
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
11
2014
On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023
Bourgain, Jean
11
2014
On toral eigenfunctions and the random wave model. Zbl 1305.60013
Bourgain, Jean
8
2014
Kloosterman sums in residue rings. Zbl 1319.11051
Bourgain, J.; Garaev, M. Z.
8
2014
Additive patterns in multiplicative subgroups. Zbl 1377.11013
Alon, Noga; Bourgain, Jean
7
2014
Perimeter of sets and BMO-type norms. Zbl 1316.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio
6
2014
Monotone Boolean functions capture their primes. Zbl 1370.11113
Bourgain, Jean
3
2014
An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015
Bourgain, J.
3
2014
On the control problem for Schrödinger operators on tori. Zbl 1318.35093
Bourgain, Jean
2
2014
Some Diophantine applications of the theory of group expansion. Zbl 1370.11082
Bourgain, Jean
1
2014
On eigenvalue spacings for the 1-D Anderson model with singular site distribution. Zbl 1319.35125
Bourgain, Jean
1
2014
On oscillatory integral operators in higher dimensions. Zbl 1301.42022
Bourgain, Jean
1
2014
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
50
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
31
2013
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
30
2013
On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017
Bourgain, J.
24
2013
On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017
Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan
21
2013
Bounds on the density of states for Schrödinger operators. Zbl 1362.35113
Bourgain, Jean; Klein, Abel
19
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.
17
2013
Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092
Bourgain, J.
17
2013
Expansion in SL\(_2(\mathbb R)\) and monotone expanders. Zbl 1268.05103
Bourgain, Jean; Yehudayoff, Amir
11
2013
Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016
Bourgain, Jean; Burq, Nicolas; Zworski, Maciej
10
2013
Prescribing the binary digits of primes. Zbl 1309.11065
Bourgain, Jean
8
2013
On the Fourier-Walsh spectrum of the Moebius function. Zbl 1336.11038
Bourgain, J.
6
2013
Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Zbl 1319.42006
Bourgain, Jean; Demeter, Ciprian
4
2013
A lower bound for the Lyapounov exponents of the random Schrödinger operator on a strip. Zbl 1432.82016
Bourgain, J.
3
2013
On Pleijel’s nodal domain theorem – Retraction notice. Zbl 06437691
Bourgain, J.
2
2013
On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025
Bourgain, J.
2
2013
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
25
2012
A spectral gap theorem in SU\((d)\). Zbl 1254.43010
Bourgain, Jean; Gamburd, Alex
23
2012
Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047
Bourgain, Jean; Rudnick, Zeév
17
2012
Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052
Bourgain, Jean; Varjú, Péter P.
15
2012
Finitely supported measures on \(\mathrm{SL}_2(\mathbb R)\) which are absolutely continuous at infinity. Zbl 1272.60004
Bourgain, Jean
10
2012
On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder. Zbl 1275.82006
Bourgain, J.
8
2012
Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Zbl 1251.35141
Bourgain, Jean; Bulut, Aynur
7
2012
Integral Apollonian circle packings and prime curvatures. Zbl 1281.52011
Bourgain, J.
5
2012
Distribution of elements of cosets of small subgroups and applications. Zbl 1290.11017
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
5
2012
A modular Szemerédi-Trotter theorem for hyperbolas. Zbl 1272.11024
Bourgain, Jean
3
2012
On representation of integers by binary quadratic forms. Zbl 1294.11040
Bourgain, Jean; Fuchs, Elena
2
2012
Partial quotients and representation of rational numbers. Zbl 1345.11007
Bourgain, Jean
2
2012
Monotone expansion. Zbl 1286.68369
Bourgain, Jean; Yehudayoff, Amir
1
2012
Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010
Bourgain, Jean; Guth, Larry
78
2011
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
49
2011
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
41
2011
...and 355 more Documents
all top 5

Cited by 5,048 Authors

200 Bourgain, Jean
90 Shparlinski, Igor E.
52 Tao, Terence
45 Tzvetkov, Nikolay
37 Naor, Assaf
35 Oh, Tadahiro
33 Iosevich, Alex
32 Brézis, Haïm
31 Damanik, David
31 Shkredov, Il’ya Dmitrievich
30 Berti, Massimiliano
29 Kenig, Carlos Eduardo
29 Lee, Sanghyuk
27 Geng, Jiansheng
27 Himonas, A. Alexandrou
26 Miao, Changxing
25 Mironescu, Petru
25 Tomczak-Jaegermann, Nicole
24 Nguyen, Hoai-Minh
23 Guo, Zihua
23 Procesi, Michela
22 Koldobsky, Alexander L.
22 You, Jiangong
22 Zhang, Bingyu
21 Chang, Mei-Chu
21 Guo, Boling
21 Ponce, Gustavo
21 Raphael, Pierre
21 Yuan, Xiaoping
20 Cui, Shangbin
20 Jitomirskaya, Svetlana Ya.
20 Paouris, Grigoris
20 Van Schaftingen, Jean
20 Vega, Luis
19 Colliander, James E.
19 Veselić, Ivan
18 Demeter, Ciprian
18 Garaev, Moubariz Z.
18 Huo, Zhaohui
18 Koh, Doowon
18 Linares, Felipe
18 Staffilani, Gigliola
18 Yan, Wei
17 Betancor Perez, Jorge Juan
17 Carvajal, Xavier Paredes
17 Kontorovich, Alex V.
17 Panthee, Mahendra
17 Sogge, Christopher D.
16 Giannopoulos, Apostolos A.
16 Konyagin, Sergeĭ Vladimirovich
16 Korolëv, Maksim Aleksandrovich
16 Li, Yongsheng
16 Schlag, Wilhelm
16 Vinh, Le Anh
16 Wang, Baoxiang
15 Bona, Jerry Lloyd
15 Erdoğan, Mehmet Burak
15 Merle, Frank
15 Milman, Vitali D.
15 Pajor, Alain
15 Pisier, Gilles
15 Shakhmurov, Veli B.
15 Vargas, Ana M.
15 Zheng, Jiqiang
14 Acosta Vigil, María Dolores
14 Burq, Nicolas
14 Guth, Lawrence David
14 Hofmann, Steve
14 Kalton, Nigel John
14 Kim, Sun Kwang
14 Martel, Yvan
14 Mirek, Mariusz
14 Molinet, Luc
14 Pham Van Thang
14 Rudnev, Misha
14 Sanders, Tom
14 Sarnak, Peter Clive
14 Schechtman, Gideon
14 Squassina, Marco
14 Torrea, José Luis
14 Visan, Monica
13 Argyros, Spiros A.
13 Castillo, Jesús M. F.
13 Grébert, Benoît
13 Herr, Sebastian
13 Isaza, Pedro
13 Johnson, William Buhmann
13 Killip, Rowan
13 Lacey, Michael T.
13 Lee, Han Ju
13 Li, Junfeng
13 Mendel, Manor
13 Orlandi, Giandomenico
13 Tzirakis, Nikolaos
13 Wang, Wei-Min
13 Xiao, Jie
13 Xu, Junxiang
13 Zvavitch, Artem
12 Casazza, Peter George
12 Castro, Alejandro J.
...and 4,948 more Authors
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Cited in 489 Serials

352 Journal of Functional Analysis
261 Journal of Mathematical Analysis and Applications
227 Israel Journal of Mathematics
227 Proceedings of the American Mathematical Society
181 Journal of Differential Equations
173 Transactions of the American Mathematical Society
156 Communications in Mathematical Physics
139 Advances in Mathematics
127 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
108 Journal d’Analyse Mathématique
102 Comptes Rendus. Mathématique. Académie des Sciences, Paris
88 Communications in Partial Differential Equations
86 Duke Mathematical Journal
73 Journal of Mathematical Physics
69 Journal of Number Theory
69 Journal of the European Mathematical Society (JEMS)
66 Mathematische Annalen
66 Geometric and Functional Analysis. GAFA
65 Mathematische Zeitschrift
62 Inventiones Mathematicae
59 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
58 Archive for Rational Mechanics and Analysis
57 Discrete and Continuous Dynamical Systems
55 Annals of Mathematics. Second Series
54 The Journal of Fourier Analysis and Applications
53 Journal of the American Mathematical Society
52 Ergodic Theory and Dynamical Systems
48 Mathematika
48 Journal de Mathématiques Pures et Appliquées. Neuvième Série
42 Revista Matemática Iberoamericana
40 Mathematical Notes
40 Calculus of Variations and Partial Differential Equations
39 Monatshefte für Mathematik
39 Acta Mathematica Sinica. English Series
38 Mathematical Proceedings of the Cambridge Philosophical Society
37 The Journal of Geometric Analysis
37 SIAM Journal on Mathematical Analysis
37 Bulletin of the American Mathematical Society. New Series
34 Bulletin of the Australian Mathematical Society
34 Communications in Contemporary Mathematics
33 Journal of Statistical Physics
32 Discrete & Computational Geometry
32 Annales Henri Poincaré
30 Positivity
30 Communications on Pure and Applied Analysis
30 Proceedings of the Steklov Institute of Mathematics
29 Acta Mathematica
29 Annales de l’Institut Fourier
28 Journal of Dynamics and Differential Equations
27 Archiv der Mathematik
27 Illinois Journal of Mathematics
25 Journal of Mathematical Sciences (New York)
24 Communications on Pure and Applied Mathematics
24 Journal of Approximation Theory
24 Indagationes Mathematicae. New Series
23 Rocky Mountain Journal of Mathematics
23 Integral Equations and Operator Theory
23 Mathematische Nachrichten
22 The Annals of Probability
22 Linear Algebra and its Applications
21 Mathematical Methods in the Applied Sciences
21 Studia Mathematica
21 Physica D
21 International Journal of Number Theory
21 Analysis & PDE
20 Arkiv för Matematik
20 Topology and its Applications
19 Acta Arithmetica
19 Probability Theory and Related Fields
19 Journal of Spectral Theory
18 Nonlinearity
18 Combinatorica
18 Forum Mathematicum
18 Journal of Evolution Equations
17 Chinese Annals of Mathematics. Series B
17 Frontiers of Mathematics in China
17 Science China. Mathematics
16 Annali di Matematica Pura ed Applicata. Serie Quarta
16 European Journal of Combinatorics
16 Finite Fields and their Applications
16 NoDEA. Nonlinear Differential Equations and Applications
16 Forum of Mathematics, Sigma
15 Compositio Mathematica
15 Glasgow Mathematical Journal
15 Journal für die Reine und Angewandte Mathematik
15 Nonlinear Analysis. Real World Applications
15 Journal of Hyperbolic Differential Equations
15 Journal of Fixed Point Theory and Applications
14 Applicable Analysis
14 Mathematics of Computation
14 Proceedings of the Edinburgh Mathematical Society. Series II
14 Abstract and Applied Analysis
13 Journal of Complexity
13 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
13 St. Petersburg Mathematical Journal
12 Geometriae Dedicata
12 Journal of Combinatorial Theory. Series A
12 Advances in Applied Mathematics
12 Potential Analysis
12 Mathematical Physics, Analysis and Geometry
...and 389 more Serials
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Cited in 61 Fields

2,195 Partial differential equations (35-XX)
1,287 Functional analysis (46-XX)
880 Number theory (11-XX)
813 Dynamical systems and ergodic theory (37-XX)
784 Harmonic analysis on Euclidean spaces (42-XX)
672 Operator theory (47-XX)
447 Probability theory and stochastic processes (60-XX)
403 Convex and discrete geometry (52-XX)
284 Measure and integration (28-XX)
266 Combinatorics (05-XX)
260 Fluid mechanics (76-XX)
253 Quantum theory (81-XX)
250 Statistical mechanics, structure of matter (82-XX)
217 Global analysis, analysis on manifolds (58-XX)
177 Real functions (26-XX)
155 Calculus of variations and optimal control; optimization (49-XX)
146 Computer science (68-XX)
138 Numerical analysis (65-XX)
131 Abstract harmonic analysis (43-XX)
130 Functions of a complex variable (30-XX)
115 Information and communication theory, circuits (94-XX)
112 Group theory and generalizations (20-XX)
112 General topology (54-XX)
109 Ordinary differential equations (34-XX)
107 Topological groups, Lie groups (22-XX)
97 Differential geometry (53-XX)
94 Linear and multilinear algebra; matrix theory (15-XX)
65 Potential theory (31-XX)
60 Approximations and expansions (41-XX)
58 Mathematical logic and foundations (03-XX)
56 Integral equations (45-XX)
56 Mechanics of deformable solids (74-XX)
55 Mechanics of particles and systems (70-XX)
50 Difference and functional equations (39-XX)
46 Geometry (51-XX)
45 Several complex variables and analytic spaces (32-XX)
42 Integral transforms, operational calculus (44-XX)
40 Algebraic geometry (14-XX)
34 Systems theory; control (93-XX)
30 Operations research, mathematical programming (90-XX)
29 Statistics (62-XX)
28 Optics, electromagnetic theory (78-XX)
19 Order, lattices, ordered algebraic structures (06-XX)
19 Biology and other natural sciences (92-XX)
18 History and biography (01-XX)
17 General and overarching topics; collections (00-XX)
17 Algebraic topology (55-XX)
16 Sequences, series, summability (40-XX)
15 Special functions (33-XX)
14 Manifolds and cell complexes (57-XX)
14 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
10 Field theory and polynomials (12-XX)
10 Geophysics (86-XX)
7 Nonassociative rings and algebras (17-XX)
6 Commutative algebra (13-XX)
5 Classical thermodynamics, heat transfer (80-XX)
5 Relativity and gravitational theory (83-XX)
2 Astronomy and astrophysics (85-XX)
1 Associative rings and algebras (16-XX)
1 Category theory; homological algebra (18-XX)
1 \(K\)-theory (19-XX)

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