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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

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)

Publications by Year

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.
471
1993
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098
Bourgain, J.
376
1993
Another look at Sobolev spaces. Zbl 1103.46310
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
207
2001
A sum-product estimate in finite fields, and applications. Zbl 1145.11306
Bourgain, Jean; Katz, N.; Tao, Terence C.
173
2004
Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161
Bourgain, Jean
171
1998
Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008
Bourgain, J.
170
1983
Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126
Bourgain, Jean
169
1998
Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178
Bourgain, Jean
166
1999
Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001
Bourgain, J.
160
2005
Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126
Bourgain, J.
152
1994
Sharp thresholds of graph properties, and the \(k\)-SAT problem (with an appendix by Jean Bourgain). Zbl 0932.05084
Friedgut, Ehud
145
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
145
1989
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006
Bourgain, J.; Milman, V. D.
132
1987
Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131
Bourgain, Jean
127
1996
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126
Bourgain, Jean
126
1999
Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037
Bourgain, Jean; Pavlović, Nataša
124
2008
Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102
Bourgain, Jean
124
1994
Averages in the plane over convex curves and maximal operators. Zbl 0626.42012
Bourgain, J.
116
1986
On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005
Bourgain, Jean; Kenig, Carlos E.
115
2005
Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030
Bourgain, Jean; Brezis, Haïm; Mironescu, Petru
111
2002
The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014
Bourgain, Jean; Demeter, Ciprian
110
2015
Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010
Bourgain, Jean; Guth, Larry
101
2011
On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086
Bourgain, J.
99
1993
On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035
Bourgain, J.; Goldstein, M.
98
2000
Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042
Bourgain, Jean; Gamburd, Alex
98
2008
On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013
Bourgain, J.
98
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
96
2016
Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014
Bourgain, J.
94
1991
Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016
Bourgain, Jean; Fremlin, David H.; Talagrand, Michel
91
1978
Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138
Bourgain, Jean
90
1997
On the equation \(\text{div }Y=f\) and application to control of phases. Zbl 1075.35006
Bourgain, Jean; Brezis, Haïm
89
2003
More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310
Bourgain, J.
87
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.
85
2006
On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013
Bourgain, J.
83
1991
Lifting in Sobolev spaces. Zbl 0967.46026
Bourgain, Jean; Brézis, Haïm; Mironescu, Petru
79
2000
Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083
Bourgain, Jean
79
1995
On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010
Bourgain, J.
78
1988
Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017
Bourgain, J.; Tzafriri, L.
76
1987
On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015
Bourgain, J.
71
1986
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
70
2017
On triples in arithmetic progression. Zbl 0959.11004
Bourgain, Jean
68
1999
Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007
Bourgain, Jean
68
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
68
2004
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019
Bourgain, J.; Jitomirskaya, S.
66
2002
A class of special L//infinity spaces. Zbl 0466.46024
Bourgain, J.; Delbaen, F.
66
1980
On dentability and the Bishop-Phelps property. Zbl 0365.46021
Bourgain, J.
64
1977
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
63
2010
The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013
Bourgain, J.
63
1986
New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061
Bourgain, Jean; Brezis, Haïm
62
2007
Approximation of zonoids by zonotopes. Zbl 0682.46008
Bourgain, J.; Lindenstrauss, J.; Milman, V.
61
1989
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
59
2013
On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010
Bourgain, Jean; Gamburd, Alex
59
2008
On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166
Bourgain, Jean
56
1996
On wellposedness of the Zakharov system. Zbl 0909.35125
Bourgain, Jean; Colliander, J.
55
1996
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086
Bourgain, J.; Garaev, M. Z.
54
2009
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
53
2011
Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096
Bourgain, J.
53
1993
The influence of variables in product spaces. Zbl 0771.60002
Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan
51
1992
On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049
Bourgain, J.
50
2003
New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039
Bourgain, J.
50
1984
On the singularity probability of discrete random matrices. Zbl 1186.60003
Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett
48
2010
On Melnikov’s persistency problem. Zbl 0897.58020
Bourgain, Jean
48
1997
Limited operators and strict cosingularity. Zbl 0601.47019
Bourgain, Jean; Diestel, Joe
47
1984
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137
Bourgain, Jean; Wang, W.
47
1997
Explicit constructions of RIP matrices and related problems. Zbl 1236.94027
Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka
45
2011
Double recurrence and almost sure convergence. Zbl 0685.28008
Bourgain, J.
45
1990
Mordell’s exponential sum estimate revisited. Zbl 1072.11063
Bourgain, J.
43
2005
On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004
Bourgain, J.
43
1987
On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026
Bourgain, Jean
42
1999
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
42
2015
On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001
Bourgain, J.
42
1991
Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential. Zbl 1089.81021
Bourgain, J.
41
2005
New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013
Bourgain, Jean; Brezis, Haïm
41
2004
A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043
Bourgain, J.
40
1986
Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150
Bourgain, Jean
39
1999
On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061
Bourgain, J.
38
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
38
2001
The discretized sum-product and projection theorems. Zbl 1234.11012
Bourgain, Jean
38
2010
On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011
Bourgain, J.
37
1988
Nonlinear Schrödinger equations. Zbl 0952.35127
Bourgain, Jean
35
1999
On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106
Bourgain, Jean
35
1997
Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023
Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm
35
2002
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
34
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
34
2013
Periodic solutions of nonlinear wave equations. Zbl 0976.35041
Bourgain, Jean
34
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
Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019
Bourgain, J.; Jitomirskaya, S.
34
2002
On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005
Bourgain, J.
34
1989
Sieving and expanders. Zbl 1217.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
33
2006
Some new estimates on oscillatory integrals. Zbl 0840.42007
Bourgain, Jean
33
1995
Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). Zbl 0853.35062
Klainerman, Sergiu; Machedon, Matei
33
1996
Roth’s theorem on progressions revisited. Zbl 1155.11011
Bourgain, Jean
33
2008
Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043
Bourgain, Jean
33
2009
On type of metric spaces. Zbl 0617.46024
Bourgain, J.; Milman, V.; Wolfson, H.
33
1986
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
32
2012
Bounded orthogonal systems and the \(\Lambda\) (p)-set problem. Zbl 0674.43004
Bourgain, J.
32
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
32
2014
Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011
Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L.
32
1985
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
32
2016
Applications of the theory of semi-embeddings to Banach space theory. Zbl 0541.46020
Bourgain, J.; Rosenthal, H. P.
31
1983
Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Zbl 07471384
Bourgain, Jean; Li, Dong
1
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
1
2020
Anderson localization for two interacting quasiperiodic particles. Zbl 07040581
Bourgain, Jean; Kachkovskiy, Ilya
8
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
4
2019
Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114
Bourgain, Jean; Li, Dong
3
2019
Beyond expansion. III: reciprocal geodesics. Zbl 1447.11079
Bourgain, Jean; Kontorovich, Alex
1
2019
Spectral gaps without the pressure condition. Zbl 1392.37065
Bourgain, Jean; Dyatlov, Semyon
19
2018
Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 07013525
Bourgain, Jean; Watt, Nigel
14
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
8
2018
On a homogenization problem. Zbl 1401.35356
Bourgain, J.
5
2018
2018 Leroy P. Steele Prizes. Zbl 1390.01053
1
2018
On a paper of Erdős and Szekeres. Zbl 1453.11040
Bourgain, Jean; Chang, Mei-Chu
1
2018
Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065
Bourgain, J.
70
2017
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016
Bourgain, Jean; Demeter, Ciprian
22
2017
A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021
Bourgain, Jean; Demeter, Ciprian
20
2017
Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071
Bourgain, Jean; Dyatlov, Semyon
18
2017
On the Vinogradov mean value. Zbl 1371.11138
Bourgain, J.
14
2017
Nonlinear Roth type theorems in finite fields. Zbl 1420.11024
Bourgain, J.; Chang, M.-C.
8
2017
Decoupling inequalities and some mean-value theorems. Zbl 1380.42008
Bourgain, Jean
7
2017
Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093
Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming
5
2017
Sidonicity and variants of Kaczmarz’s problem. (Sidonicité et un problème de Kaczmarz.) Zbl 1388.43008
Bourgain, Jean; Lewko, Mark
5
2017
Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120
Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév
5
2017
Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054
Bourgain, Jean; Kontorovich, Alex
4
2017
Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076
Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter
4
2017
On random walks in large compact Lie groups. Zbl 1370.60085
Bourgain, Jean
1
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
96
2016
A note on the Schrödinger maximal function. Zbl 1361.35151
Bourgain, J.
32
2016
BMO-type norms related to the perimeter of sets. Zbl 1352.46026
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio
17
2016
A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024
Bourgain, Jean
11
2016
Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082
Bourgain, Jean; Demeter, Ciprian
11
2016
Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
10
2016
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
9
2016
Decouplings for surfaces in \(\mathbb{R}^4\). Zbl 1332.53007
Bourgain, Jean; Demeter, Ciprian
7
2016
The essential centre of the mod a diagonalization ideal commutant of an \(n\)-tuple of commuting Hermitian operators. Zbl 1375.47011
Bourgain, Jean; Voiculescu, Dan-Virgil
5
2016
On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012
Bourgain, Jean
2
2016
On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046
Bourgain, Jean
1
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
110
2015
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266
Bourgain, Jean; Li, Dong
42
2015
Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 1480.35316
Bourgain, Jean; Li, Dong
25
2015
A new function space and applications. Zbl 1339.46028
Bourgain, Jean; Brezis, Haim; Mironescu, Petru
24
2015
A problem on sums of two squares. Zbl 1364.11091
Bombieri, Enrico; Bourgain, Jean
18
2015
Prescribing the binary digits of primes. II. Zbl 1310.11097
Bourgain, Jean
17
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
16
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
14
2015
New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013
Bourgain, Jean; Demeter, Ciprian
10
2015
On Pleijel’s nodal domain theorem. Zbl 1317.35145
Bourgain, Jean
10
2015
Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007
Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani
9
2015
The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068
Bourgain, Jean; Kontorovich, Alex
7
2015
Nodal intersections and \(L^p\) restriction theorems on the torus. Zbl 1319.58023
Bourgain, Jean; Rudnick, Zeév
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
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
32
2014
Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071
Bourgain, J.; Garaev, M. Z.
31
2014
On an endpoint Kato-Ponce inequality. Zbl 1340.42021
Bourgain, Jean; Li, Dong
28
2014
On Zaremba’s conjecture. Zbl 1370.11083
Bourgain, Jean; Kontorovich, Alex
28
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
22
2014
Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323
Bourgain, Jean; Bulut, Aynur
22
2014
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
19
2014
On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046
Bourgain, Jean; Kontorovich, Alex
18
2014
An improved estimate in the restricted isometry problem. Zbl 1323.46009
Bourgain, Jean
14
2014
On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023
Bourgain, Jean
14
2014
On toral eigenfunctions and the random wave model. Zbl 1305.60013
Bourgain, Jean
12
2014
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
11
2014
Additive patterns in multiplicative subgroups. Zbl 1377.11013
Alon, Noga; Bourgain, Jean
9
2014
Kloosterman sums in residue rings. Zbl 1319.11051
Bourgain, J.; Garaev, M. Z.
8
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
An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015
Bourgain, J.
4
2014
Monotone Boolean functions capture their primes. Zbl 1370.11113
Bourgain, Jean
3
2014
On the control problem for Schrödinger operators on tori. Zbl 1318.35093
Bourgain, Jean
2
2014
On oscillatory integral operators in higher dimensions. Zbl 1301.42022
Bourgain, Jean
1
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 the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians. Zbl 1319.35126
Bourgain, Jean
1
2014
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
59
2013
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039
Bourgain, J.
34
2013
On the Schrödinger maximal function in higher dimension. Zbl 1291.35253
Bourgain, Jean
34
2013
On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017
Bourgain, J.
30
2013
On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017
Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan
26
2013
Bounds on the density of states for Schrödinger operators. Zbl 1362.35113
Bourgain, Jean; Klein, Abel
23
2013
Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092
Bourgain, J.
19
2013
Expansion in SL\(_2(\mathbb R)\) and monotone expanders. Zbl 1268.05103
Bourgain, Jean; Yehudayoff, Amir
15
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.
14
2013
Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016
Bourgain, Jean; Burq, Nicolas; Zworski, Maciej
12
2013
Prescribing the binary digits of primes. Zbl 1309.11065
Bourgain, Jean
9
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 the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025
Bourgain, J.
2
2013
On Pleijel’s nodal domain theorem – Retraction notice. Zbl 1464.35160
Bourgain, J.
2
2013
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
32
2012
A spectral gap theorem in SU\((d)\). Zbl 1254.43010
Bourgain, Jean; Gamburd, Alex
30
2012
Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047
Bourgain, Jean; Rudnick, Zeév
19
2012
Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052
Bourgain, Jean; Varjú, Péter P.
17
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.
9
2012
Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Zbl 1251.35141
Bourgain, Jean; Bulut, Aynur
8
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
...and 363 more Documents
all top 5

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
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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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