×

Bourgain, Jean (b. 1954 d. 2018)

Author ID: bourgain.jean Recent zbMATH articles by "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)
all top 5

Co-Authors

307 single-authored
18 Milman, Vitali D.
15 Brézis, Haïm
14 Demeter, Ciprian
14 Konyagin, Sergeĭ Vladimirovich
13 Gamburd, Alexander
12 Kontorovich, Alex V.
11 Lindenstrauss, Joram
10 Chang, Mei-Chu
10 Shparlinski, Igor E.
9 Sarnak, Peter Clive
8 Rudnick, Zeév
7 Mironescu, Petru
7 Tzafriri, Lior
6 Garaev, Moubariz Z.
5 Alon, Noga
5 Gromov, Mikhael Leonidovich
5 Li, Dong
5 Lindenstrauss, Elon
5 Mirek, Mariusz
5 Stein, Elias Menachem
4 Bombieri, Enrico
4 Bulut, Aynur
4 Connes, Alain
4 Kalai, Gil
4 Rosenthal, Haskell P.
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 Kahane, Jean-Pierre
3 Schlag, Wilhelm
3 Talagrand, Michel
2 Ambrosio, Luigi
2 Clozel, Laurent
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 Kahn, Jeff D.
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 Watt, Nigel
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 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 Kaloshin, Vadim Yu.
...and 52 more Co-Authors
all top 5

Serials

45 Israel Journal of Mathematics
34 Geometric and Functional Analysis. GAFA
33 Journal d’Analyse Mathématique
30 Comptes Rendus. Mathématique. Académie des Sciences, Paris
24 IMRN. International Mathematics Research Notices
18 Bulletin de la Société Matheḿatique de Belgique. Série B
12 Communications in Mathematical Physics
12 Comptes Rendus de l’Académie des Sciences. Série I
11 Studia Mathematica
11 Inventiones Mathematicae
11 Journal of the European Mathematical Society (JEMS)
9 Journal of Functional Analysis
9 Annals of Mathematics. Second Series
8 Proceedings of the American Mathematical Society
8 Journal of the American Mathematical Society
6 Acta Mathematica
6 Annales de l’Institut Fourier
6 Transactions of the American Mathematical Society
5 Acta Arithmetica
5 Duke Mathematical Journal
4 Journal of Statistical Physics
4 American Journal of Mathematics
4 Fundamenta Mathematicae
4 Journal of the London Mathematical Society. Second Series
4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A
3 Illinois Journal of Mathematics
3 Journal für die Reine und Angewandte Mathematik
3 Mathematische Nachrichten
3 Notices of the American Mathematical Society
3 Proceedings of the Steklov Institute of Mathematics
2 Communications on Pure and Applied Mathematics
2 Mathematical Notes
2 Russian Mathematical Surveys
2 Arkiv för Matematik
2 Colloquium Mathematicum
2 Compositio Mathematica
2 Publications Mathématiques
2 Integral Equations and Operator Theory
2 Memoirs of the American Mathematical Society
2 Pacific Journal of Mathematics
2 Ergodic Theory and Dynamical Systems
2 Selecta Mathematica. New Series
2 Discrete and Continuous Dynamical Systems
2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
2 Annals of Mathematics Studies
2 Modern Birkhäuser Classics
1 Letters in Mathematical Physics
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Mathematics of Computation
1 Advances in Mathematics
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Boletim da Sociedade Brasileira de Matemática
1 Bulletin de la Société Mathématique de France
1 Michigan Mathematical Journal
1 Real Analysis Exchange
1 SIAM Journal on Computing
1 Simon Stevin
1 Journal of Operator Theory
1 Chinese Annals of Mathematics. Series B
1 Bulletin of the Iranian Mathematical Society
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Discrete & Computational Geometry
1 Revista Matemática Iberoamericana
1 SIAM Journal on Discrete Mathematics
1 Differential and Integral Equations
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Proceedings of the National Academy of Sciences of the United States of America
1 Computational Complexity
1 Mathematical Research Letters
1 Sbornik: Mathematics
1 Izvestiya: Mathematics
1 The Journal of Fourier Analysis and Applications
1 Annales Henri Poincaré
1 Moscow Mathematical Journal
1 International Journal of Number Theory
1 Colloquium Publications. American Mathematical Society
1 Lecture Notes in Mathematics
1 Journal of Spectral Theory
1 Forum of Mathematics, Pi
1 Discrete Analysis
all top 5

Fields

152 Number theory (11-XX)
139 Functional analysis (46-XX)
96 Partial differential equations (35-XX)
91 Harmonic analysis on Euclidean spaces (42-XX)
62 Operator theory (47-XX)
43 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 Group theory and generalizations (20-XX)
9 Computer science (68-XX)
8 History and biography (01-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 Field theory and polynomials (12-XX)
3 Sequences, series, summability (40-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Differential geometry (53-XX)
2 Algebraic topology (55-XX)
2 Fluid mechanics (76-XX)
1 Commutative algebra (13-XX)
1 Integral transforms, operational calculus (44-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Numerical analysis (65-XX)
1 Mechanics of particles and systems (70-XX)
1 Operations research, mathematical programming (90-XX)
1 Systems theory; control (93-XX)

Publications by Year

Citations contained in zbMATH Open

473 Publications have been cited 13,902 times in 8,296 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.
550
1993
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098
Bourgain, J.
447
1993
Another look at Sobolev spaces. Zbl 1103.46310
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
288
2001
Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001
Bourgain, J.
226
2005
Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178
Bourgain, Jean
211
1999
Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126
Bourgain, J.
193
1994
Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161
Bourgain, Jean
193
1998
Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126
Bourgain, Jean
191
1998
A sum-product estimate in finite fields, and applications. Zbl 1145.11306
Bourgain, Jean; Katz, N.; Tao, Terence C.
191
2004
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
184
1989
Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008
Bourgain, J.
182
1983
The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
178
2015
Sharp thresholds of graph properties, and the \(k\)-SAT problem (with an appendix by Jean Bourgain). Zbl 0932.05084
Friedgut, Ehud
174
1999
Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131
Bourgain, Jean
170
1996
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006
Bourgain, J.; Milman, V. D.
147
1987
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126
Bourgain, Jean
147
1999
Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037
Bourgain, Jean; Pavlović, Nataša
147
2008
Averages in the plane over convex curves and maximal operators. Zbl 0626.42012
Bourgain, J.
146
1986
On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005
Bourgain, Jean; Kenig, Carlos E.
139
2005
Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010
Bourgain, Jean; Guth, Larry
139
2011
Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102
Bourgain, Jean
138
1994
Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030
Bourgain, Jean; Brezis, Haïm; Mironescu, Petru
135
2002
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
132
2016
On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035
Bourgain, J.; Goldstein, M.
120
2000
Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042
Bourgain, Jean; Gamburd, Alex
118
2008
On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013
Bourgain, J.
113
1985
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
110
2017
Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014
Bourgain, J.
110
1991
On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086
Bourgain, J.
108
1993
On the equation \(\operatorname{div}Y=f\) and application to control of phases. Zbl 1075.35006
Bourgain, Jean; Brezis, Haïm
107
2003
More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310
Bourgain, J.
106
2005
On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013
Bourgain, J.
100
1991
Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138
Bourgain, Jean
98
1997
Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016
Bourgain, Jean; Fremlin, David H.; Talagrand, Michel
97
1978
On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010
Bourgain, J.
95
1988
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.
90
2006
Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083
Bourgain, Jean
89
1995
Lifting in Sobolev spaces. Zbl 0967.46026
Bourgain, Jean; Brézis, Haïm; Mironescu, Petru
86
2000
Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017
Bourgain, J.; Tzafriri, L.
84
1987
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019
Bourgain, J.; Jitomirskaya, S.
83
2002
On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015
Bourgain, J.
83
1986
Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007
Bourgain, Jean
80
1996
The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013
Bourgain, J.
78
1986
New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061
Bourgain, Jean; Brezis, Haïm
77
2007
On triples in arithmetic progression. Zbl 0959.11004
Bourgain, Jean
76
1999
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
76
2010
On dentability and the Bishop-Phelps property. Zbl 0365.46021
Bourgain, J.
74
1977
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
74
2013
Approximation of zonoids by zonotopes. Zbl 0682.46008
Bourgain, J.; Lindenstrauss, J.; Milman, V.
74
1989
\(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
72
2004
A class of special \(L_\infty\) spaces. Zbl 0466.46024
Bourgain, J.; Delbaen, F.
71
1980
On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010
Bourgain, Jean; Gamburd, Alex
70
2008
On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166
Bourgain, Jean
64
1996
On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049
Bourgain, J.
64
2003
On wellposedness of the Zakharov system. Zbl 0909.35125
Bourgain, Jean; Colliander, J.
63
1996
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
60
2015
Double recurrence and almost sure convergence. Zbl 0685.28008
Bourgain, J.
59
1990
On the singularity probability of discrete random matrices. Zbl 1186.60003
Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett
58
2010
Limited operators and strict cosingularity. Zbl 0601.47019
Bourgain, Jean; Diestel, Joe
57
1984
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
57
2011
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086
Bourgain, J.; Garaev, M. Z.
57
2009
On Melnikov’s persistency problem. Zbl 0897.58020
Bourgain, Jean
56
1997
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137
Bourgain, Jean; Wang, W.
56
1997
The influence of variables in product spaces. Zbl 0771.60002
Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan
56
1992
Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096
Bourgain, J.
56
1993
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
55
2016
A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043
Bourgain, J.
54
1986
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
52
2013
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
52
2011
New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039
Bourgain, J.
51
1984
On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011
Bourgain, J.
51
1988
The discretized sum-product and projection theorems. Zbl 1234.11012
Bourgain, Jean
50
2010
Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
49
2002
Nonlinear Schrödinger equations. Zbl 0952.35127
Bourgain, Jean
49
1999
Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150
Bourgain, Jean
48
1999
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.
48
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
48
2001
New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013
Bourgain, Jean; Brezis, Haïm
48
2004
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
48
2013
On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026
Bourgain, Jean
47
1999
Mordell’s exponential sum estimate revisited. Zbl 1072.11063
Bourgain, J.
46
2005
On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004
Bourgain, J.
45
1987
On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061
Bourgain, J.
45
2005
Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019
Bourgain, J.; Jitomirskaya, S.
45
2002
On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001
Bourgain, J.
45
1991
Some new estimates on oscillatory integrals. Zbl 0840.42007
Bourgain, Jean
44
1995
Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043
Bourgain, Jean
43
2009
On Zaremba’s conjecture. Zbl 1370.11083
Bourgain, Jean; Kontorovich, Alex
42
2014
On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005
Bourgain, J.
42
1989
On an endpoint Kato-Ponce inequality. Zbl 1340.42021
Bourgain, Jean; Li, Dong
41
2014
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071
Bourgain, J.; Garaev, M. Z.
39
2014
Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 1480.35316
Bourgain, Jean; Li, Dong
38
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
38
2014
On type of metric spaces. Zbl 0617.46024
Bourgain, J.; Milman, V.; Wolfson, H.
38
1986
Invariant measures for the Gross-Pitaevskii equation. (Invariant measures for the Gross-Piatevskii equation.) Zbl 0906.35095
Bourgain, Jean
38
1997
A spectral gap theorem in SU\((d)\). Zbl 1254.43010
Bourgain, Jean; Gamburd, Alex
38
2012
Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011
Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L.
38
1985
On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017
Bourgain, J.
37
2013
Periodic solutions of nonlinear wave equations. Zbl 0976.35041
Bourgain, Jean
37
1999
Anderson localization for quasi-periodic lattice Schrödinger operators on \(\mathbb Z^d\), \(d\) arbitrary. Zbl 1152.82311
Bourgain, Jean
37
2007
Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Zbl 1490.35257
Bourgain, Jean; Li, Dong
4
2021
On the Hardy-Littlewood maximal functions in high dimensions: continuous and discrete perspective. Zbl 1479.42046
Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej
2
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
5
2020
Decouplings for real analytic surfaces of revolution. Zbl 1446.42009
Bourgain, Jean; Demeter, Ciprian; Kemp, Dominique
2
2020
Three applications of the Siegel mass formula. Zbl 1465.11174
Bourgain, Jean; Demeter, Ciprian
1
2020
Anderson localization for two interacting quasiperiodic particles. Zbl 07040581
Bourgain, Jean; Kachkovskiy, Ilya
13
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
8
2019
Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114
Bourgain, Jean; Li, Dong
7
2019
Beyond expansion. III: reciprocal geodesics. Zbl 1447.11079
Bourgain, Jean; Kontorovich, Alex
2
2019
Spectral gaps without the pressure condition. Zbl 1392.37065
Bourgain, Jean; Dyatlov, Semyon
25
2018
Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 1486.11117
Bourgain, Jean; Watt, Nigel
21
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
13
2018
On a homogenization problem. Zbl 1401.35356
Bourgain, J.
7
2018
On a paper of Erdős and Szekeres. Zbl 1453.11040
Bourgain, Jean; Chang, Mei-Chu
4
2018
Beyond expansion. IV: Traces of thin semigroups. Zbl 1428.11128
Bourgain, Jean; Kontorovich, Alex
1
2018
2018 Leroy P. Steele Prizes. Zbl 1390.01053
1
2018
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
110
2017
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016
Bourgain, Jean; Demeter, Ciprian
35
2017
Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071
Bourgain, Jean; Dyatlov, Semyon
31
2017
A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021
Bourgain, Jean; Demeter, Ciprian
27
2017
On the Vinogradov mean value. Zbl 1371.11138
Bourgain, J.
21
2017
Decoupling inequalities and some mean-value theorems. Zbl 1380.42008
Bourgain, Jean
11
2017
Nonlinear Roth type theorems in finite fields. Zbl 1420.11024
Bourgain, J.; Chang, M.-C.
10
2017
Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076
Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter
8
2017
Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120
Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév
8
2017
Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093
Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming
7
2017
Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054
Bourgain, Jean; Kontorovich, Alex
5
2017
Sidonicity and variants of Kaczmarz’s problem. (Sidonicité et un problème de Kaczmarz.) Zbl 1388.43008
Bourgain, Jean; Lewko, Mark
5
2017
On a problem of Farrell and Vershynin in random matrix theory. Zbl 1366.60008
Bourgain, Jean
2
2017
On random walks in large compact Lie groups. Zbl 1370.60085
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
132
2016
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
55
2016
Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
23
2016
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
18
2016
Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082
Bourgain, Jean; Demeter, Ciprian
17
2016
A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024
Bourgain, Jean
16
2016
Decouplings for surfaces in \(\mathbb{R}^4\). Zbl 1332.53007
Bourgain, Jean; Demeter, Ciprian
11
2016
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
11
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
6
2016
On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012
Bourgain, Jean
3
2016
On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046
Bourgain, Jean
2
2016
Affine extractors over large fields with exponential error. Zbl 1419.11132
Bourgain, Jean; Dvir, Zeev; Leeman, Ethan
1
2016
The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
178
2015
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
60
2015
Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 1480.35316
Bourgain, Jean; Li, Dong
38
2015
A new function space and applications. Zbl 1339.46028
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
28
2015
Prescribing the binary digits of primes. II. Zbl 1310.11097
Bourgain, Jean
24
2015
A problem on sums of two squares. Zbl 1364.11091
Bombieri, Enrico; Bourgain, Jean
23
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
21
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
17
2015
New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013
Bourgain, Jean; Demeter, Ciprian
16
2015
Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007
Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani
13
2015
On Pleijel’s nodal domain theorem. Zbl 1317.35145
Bourgain, Jean
10
2015
Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
9
2015
Nodal intersections and \(L^p\) restriction theorems on the torus. Zbl 1319.58023
Bourgain, Jean; Rudnick, Zeév
9
2015
The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068
Bourgain, Jean; Kontorovich, Alex
7
2015
A remark on solutions of the Pell equation. Zbl 1372.11039
Bourgain, J.
5
2015
A note on Lyapunov exponents of deterministic strongly mixing potentials. Zbl 1318.82021
Bourgain, Jean; Bourgain-Chang, Eric
2
2015
Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1321.68431
Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani
1
2015
On Zaremba’s conjecture. Zbl 1370.11083
Bourgain, Jean; Kontorovich, Alex
42
2014
On an endpoint Kato-Ponce inequality. Zbl 1340.42021
Bourgain, Jean; Li, Dong
41
2014
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071
Bourgain, J.; Garaev, M. Z.
39
2014
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
38
2014
Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323
Bourgain, Jean; Bulut, Aynur
26
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
26
2014
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
26
2014
On toral eigenfunctions and the random wave model. Zbl 1305.60013
Bourgain, Jean
20
2014
On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023
Bourgain, Jean
20
2014
On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046
Bourgain, Jean; Kontorovich, Alex
20
2014
An improved estimate in the restricted isometry problem. Zbl 1323.46009
Bourgain, Jean
17
2014
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
13
2014
Additive patterns in multiplicative subgroups. Zbl 1377.11013
Alon, Noga; Bourgain, Jean
12
2014
Kloosterman sums in residue rings. Zbl 1319.11051
Bourgain, J.; Garaev, M. Z.
9
2014
An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015
Bourgain, J.
5
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
5
2014
Monotone Boolean functions capture their primes. Zbl 1370.11113
Bourgain, Jean
3
2014
On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians. Zbl 1319.35126
Bourgain, Jean
2
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
2
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.
74
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
52
2013
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
48
2013
On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017
Bourgain, J.
37
2013
Bounds on the density of states for Schrödinger operators. Zbl 1362.35113
Bourgain, Jean; Klein, Abel
32
2013
On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017
Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan
27
2013
Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016
Bourgain, Jean; Burq, Nicolas; Zworski, Maciej
22
2013
Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092
Bourgain, J.
22
2013
Expansion in SL\(_2(\mathbb R)\) and monotone expanders. Zbl 1268.05103
Bourgain, Jean; Yehudayoff, Amir
20
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.
16
2013
Prescribing the binary digits of primes. Zbl 1309.11065
Bourgain, Jean
13
2013
Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Zbl 1319.42006
Bourgain, Jean; Demeter, Ciprian
8
2013
On the Fourier-Walsh spectrum of the Moebius function. Zbl 1336.11038
Bourgain, J.
6
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 1464.35160
Bourgain, J.
2
2013
On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025
Bourgain, J.
2
2013
A spectral gap theorem in SU\((d)\). Zbl 1254.43010
Bourgain, Jean; Gamburd, Alex
38
2012
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
37
2012
Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052
Bourgain, Jean; Varjú, Péter P.
26
2012
...and 373 more Documents
all top 5

Cited by 6,371 Authors

208 Bourgain, Jean
106 Shparlinski, Igor E.
61 Tzvetkov, Nikolay
57 Tao, Terence
51 Oh, Tadahiro
41 Naor, Assaf
40 Shkredov, Il’ya Dmitrievich
39 Iosevich, Alex
39 Lee, Sanghyuk
37 Damanik, David
36 Geng, Jiansheng
35 Himonas, A. Alexandrou
33 Brézis, Haïm
33 Kenig, Carlos Eduardo
33 Miao, Changxing
30 Berti, Massimiliano
29 Betancor Perez, Jorge Juan
29 You, Jiangong
28 Nguyen, Hoai-Minh
28 Procesi, Michela
28 Van Schaftingen, Jean
28 Yan, Wei
27 Guo, Boling
27 Zhang, Bingyu
26 Guo, Zihua
26 Koldobsky, Alexander L.
26 Mironescu, Petru
25 Raphael, Pierre
25 Tomczak-Jaegermann, Nicole
25 Vega, Luis
24 Jitomirskaya, Svetlana Yakovlevna
23 Korolëv, Maksim Aleksandrovich
23 Mirek, Mariusz
23 Ponce, Gustavo
23 Staffilani, Gigliola
23 Yuan, Xiaoping
22 Koh, Doowon
22 Panthee, Mahendra
22 Sogge, Christopher D.
21 Chang, Mei-Chu
21 Kontorovich, Alex V.
21 Paouris, Grigoris
21 Veselić, Ivan
21 Zheng, Jiqiang
20 Carvajal, Xavier Paredes
20 Cui, Shangbin
20 Demeter, Ciprian
20 Linares, Felipe
20 Rudnev, Misha
20 Schlag, Wilhelm
20 Vinh, Le Anh
19 Burq, Nicolas
19 Colliander, James E.
19 Garaev, Moubariz Z.
19 Li, Yongsheng
19 Montalto, Riccardo
19 Pham Van Thang
19 Wang, Baoxiang
19 Wang, Yuzhao
18 Giannopoulos, Apostolos A.
18 Guth, Lawrence David
18 Huo, Zhaohui
18 Milman, Vitali D.
18 Rodríguez-Mesa, Lourdes
18 Schlumprecht, Thomas
18 Shakhmurov, Veli B.
18 Squassina, Marco
17 Grébert, Benoît
17 Kim, Sun Kwang
17 Lacey, Michael T.
17 Li, Junfeng
17 Magyar, Akos
17 Sarnak, Peter Clive
17 Xu, Junxiang
17 Yung, Polam
16 Du, Qiang
16 Herr, Sebastian
16 Konyagin, Sergeĭ Vladimirovich
16 Lemańczyk, Mariusz
16 Merle, Frank
16 Pisier, Gilles
16 Visan, Monica
16 Zvavitch, Artem
15 Bona, Jerry Lloyd
15 Castillo, Jesús M. F.
15 Castro, Alejandro J.
15 Erdoğan, Mehmet Burak
15 González Ortiz, Manuel
15 Martel, Yvan
15 Orlandi, Giandomenico
15 Pajor, Alain
15 Schechtman, Gideon
15 Seeger, Andreas
15 Shen, Chun-Yen
15 Spector, Daniel E.
15 Sukochev, Fedor Anatol’evich
15 Tzirakis, Nikolaos
15 Vargas, Ana M.
14 Acosta Vigil, María Dolores
14 Albiac, Fernando
...and 6,271 more Authors
all top 5

Cited in 577 Serials

418 Journal of Functional Analysis
309 Journal of Mathematical Analysis and Applications
265 Proceedings of the American Mathematical Society
237 Israel Journal of Mathematics
216 Journal of Differential Equations
208 Communications in Mathematical Physics
206 Transactions of the American Mathematical Society
188 Advances in Mathematics
153 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
139 Journal d’Analyse Mathématique
107 Comptes Rendus. Mathématique. Académie des Sciences, Paris
100 Communications in Partial Differential Equations
98 Duke Mathematical Journal
97 Journal of Mathematical Physics
88 Mathematische Zeitschrift
86 Discrete and Continuous Dynamical Systems
84 Journal of Number Theory
84 Journal of the European Mathematical Society (JEMS)
80 Mathematische Annalen
78 Archive for Rational Mechanics and Analysis
78 Geometric and Functional Analysis. GAFA
77 Inventiones Mathematicae
71 The Journal of Geometric Analysis
69 The Journal of Fourier Analysis and Applications
67 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
65 Mathematika
62 Ergodic Theory and Dynamical Systems
62 Calculus of Variations and Partial Differential Equations
61 Revista Matemática Iberoamericana
59 Journal of the American Mathematical Society
59 Annals of Mathematics. Second Series
57 Journal de Mathématiques Pures et Appliquées. Neuvième Série
56 SIAM Journal on Mathematical Analysis
52 Communications on Pure and Applied Analysis
50 Mathematical Proceedings of the Cambridge Philosophical Society
49 Analysis & PDE
48 Acta Mathematica Sinica. English Series
47 Journal of Dynamics and Differential Equations
47 Annales Henri Poincaré
45 Mathematical Notes
44 Communications in Contemporary Mathematics
42 Monatshefte für Mathematik
42 Bulletin of the American Mathematical Society. New Series
40 Journal of Statistical Physics
39 Discrete & Computational Geometry
38 Bulletin of the Australian Mathematical Society
37 Studia Mathematica
37 Mathematische Nachrichten
36 Annales de l’Institut Fourier
36 Proceedings of the Steklov Institute of Mathematics
35 Acta Arithmetica
35 Positivity
35 Journal of Evolution Equations
33 Journal of Mathematical Sciences (New York)
31 Archiv der Mathematik
29 Rocky Mountain Journal of Mathematics
29 Acta Mathematica
29 The Annals of Probability
29 International Journal of Number Theory
28 Communications on Pure and Applied Mathematics
28 Illinois Journal of Mathematics
28 Journal of Spectral Theory
27 Forum Mathematicum
27 Indagationes Mathematicae. New Series
26 Mathematical Methods in the Applied Sciences
26 Nonlinearity
26 Journal of Approximation Theory
26 Finite Fields and their Applications
25 Integral Equations and Operator Theory
25 Combinatorica
25 Linear Algebra and its Applications
25 Forum of Mathematics, Sigma
23 Journal of the London Mathematical Society. Second Series
23 Probability Theory and Related Fields
23 Science China. Mathematics
22 Annali di Matematica Pura ed Applicata. Serie Quarta
22 Physica D
22 Potential Analysis
22 NoDEA. Nonlinear Differential Equations and Applications
21 Applicable Analysis
21 Mathematics of Computation
21 Topology and its Applications
21 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
20 European Journal of Combinatorics
20 Nonlinear Analysis. Real World Applications
20 Journal of Hyperbolic Differential Equations
20 Frontiers of Mathematics in China
19 Arkiv för Matematik
19 Proceedings of the Edinburgh Mathematical Society. Series II
19 Acta Mathematica Hungarica
19 The Ramanujan Journal
18 Journal für die Reine und Angewandte Mathematik
18 Results in Mathematics
18 Chinese Annals of Mathematics. Series B
18 Discrete and Continuous Dynamical Systems. Series B
18 Mediterranean Journal of Mathematics
17 Indiana University Mathematics Journal
17 Journal of Complexity
17 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
17 Combinatorics, Probability and Computing
...and 477 more Serials
all top 5

Cited in 61 Fields

2,960 Partial differential equations (35-XX)
1,578 Functional analysis (46-XX)
1,267 Number theory (11-XX)
1,152 Harmonic analysis on Euclidean spaces (42-XX)
1,085 Dynamical systems and ergodic theory (37-XX)
855 Operator theory (47-XX)
634 Probability theory and stochastic processes (60-XX)
510 Convex and discrete geometry (52-XX)
410 Measure and integration (28-XX)
381 Combinatorics (05-XX)
381 Fluid mechanics (76-XX)
375 Quantum theory (81-XX)
338 Statistical mechanics, structure of matter (82-XX)
293 Global analysis, analysis on manifolds (58-XX)
270 Real functions (26-XX)
205 Calculus of variations and optimal control; optimization (49-XX)
205 Numerical analysis (65-XX)
201 Computer science (68-XX)
183 Functions of a complex variable (30-XX)
161 Information and communication theory, circuits (94-XX)
156 Group theory and generalizations (20-XX)
153 Abstract harmonic analysis (43-XX)
150 Topological groups, Lie groups (22-XX)
149 Linear and multilinear algebra; matrix theory (15-XX)
140 Differential geometry (53-XX)
137 Ordinary differential equations (34-XX)
128 General topology (54-XX)
91 Approximations and expansions (41-XX)
86 Potential theory (31-XX)
81 Mechanics of deformable solids (74-XX)
79 Geometry (51-XX)
75 Integral equations (45-XX)
74 Mechanics of particles and systems (70-XX)
73 Mathematical logic and foundations (03-XX)
67 Difference and functional equations (39-XX)
64 Algebraic geometry (14-XX)
62 Integral transforms, operational calculus (44-XX)
59 Systems theory; control (93-XX)
58 Several complex variables and analytic spaces (32-XX)
48 Statistics (62-XX)
44 Operations research, mathematical programming (90-XX)
38 Optics, electromagnetic theory (78-XX)
30 General and overarching topics; collections (00-XX)
27 Special functions (33-XX)
26 History and biography (01-XX)
25 Order, lattices, ordered algebraic structures (06-XX)
25 Biology and other natural sciences (92-XX)
21 Manifolds and cell complexes (57-XX)
20 Algebraic topology (55-XX)
18 Sequences, series, summability (40-XX)
16 Geophysics (86-XX)
16 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
11 Field theory and polynomials (12-XX)
6 Commutative algebra (13-XX)
6 Associative rings and algebras (16-XX)
6 Nonassociative rings and algebras (17-XX)
6 Relativity and gravitational theory (83-XX)
5 Classical thermodynamics, heat transfer (80-XX)
3 \(K\)-theory (19-XX)
2 Astronomy and astrophysics (85-XX)
1 Category theory; homological algebra (18-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.