# Jean Bourgain

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Belgian mathematician and Fields Medalist

## Jean Bourgain's AcademicInfluence.com Rankings

Jean Bourgainmathematics Degrees

Mathematics

#49

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#146

Historical Rank

Measure Theory

#45

World Rank

#79

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Mathematics

## Jean Bourgain's Degrees

- PhD Mathematics Université libre de Bruxelles

## Why Is Jean Bourgain Influential?

(Suggest an Edit or Addition)According to Wikipedia, Jean Louis, baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.

## Jean Bourgain's Published Works

### Published Works

- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations (1993) (1735)
- On lipschitz embedding of finite metric spaces in Hilbert space (1985) (724)
- On nonlinear Schrödinger equations (1998) (617)
- Another look at Sobolev spaces (2001) (513)
- Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity (1998) (504)
- A sum-product estimate in finite fields, and applications (2003) (498)
- Green's Function Estimates for Lattice Schrödinger Operators and Applications. (2004) (445)
- Some remarks on Banach spaces in which martingale difference sequences are unconditional (1983) (445)
- Pointwise ergodic theorems for arithmetic sets (1989) (422)
- Periodic nonlinear Schrödinger equation and invariant measures (1994) (390)
- QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS (1998) (358)
- New volume ratio properties for convex symmetric bodies in ℝn (1987) (332)
- Bounds on Oscillatory Integral Operators Based on Multilinear Estimates (2010) (304)
- Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case (1999) (303)
- MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS (2005) (303)
- Besicovitch type maximal operators and applications to fourier analysis (1991) (297)
- Averages in the plane over convex curves and maximal operators (1986) (287)
- Uniform expansion bounds for Cayley graphs of SL2(Fp) (2008) (285)
- Ill-posedness of the Navier-Stokes equations in a critical space in 3D (2008) (275)
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations (1993) (271)
- Mathematical aspects of nonlinear dispersive equations (2007) (271)
- Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE (1994) (266)
- On localization in the continuous Anderson-Bernoulli model in higher dimension (2005) (264)
- The proof of the $l^2$ Decoupling Conjecture (2014) (260)
- On Triples in Arithmetic Progression (1999) (257)
- Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015) (255)
- On the distribution of polynomials on high dimensional convex sets (1991) (252)
- Approximation of zonoids by zonotopes (1989) (235)
- Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order (2006) (228)
- On the maximal ergodic theorem for certain subsets of the integers (1988) (226)
- Explicit constructions of RIP matrices and related problems (2010) (226)
- Limiting embedding theorems forWs,p whens ↑ 1 and applications (2002) (221)
- On nonperturbative localization with quasi-periodic potential (2000) (217)
- Invertibility of ‘large’ submatrices with applications to the geometry of Banach spaces and harmonic analysis (1987) (215)
- ON HIGH DIMENSIONAL MAXIMAL FUNCTIONS ASSOCIATED TO CONVEX BODIES (1986) (214)
- Periodic Korteweg de Vries equation with measures as initial data (1997) (213)
- Decoupling, exponential sums and the Riemann zeta function (2014) (206)
- Pointwise Compact Sets of Baire-Measurable Functions (1978) (204)
- Continuity of the Lyapunov Exponent for Quasiperiodic Operators with Analytic Potential (2001) (195)
- Lifting in Sobolev spaces (2000) (194)
- Affine linear sieve, expanders, and sum-product (2010) (189)
- Global Solutions of Nonlinear Schrodinger Equations (1999) (183)
- The metrical interpretation of superreflexivity in banach spaces (1986) (181)
- Construction of periodic solutions of nonlinear wave equations in higher dimension (1995) (170)
- Construction of approximative and almost periodic solutions of perturbed linear schrödinger and wave equations (1996) (169)
- On the spectral gap for finitely-generated subgroups of SU(2) (2007) (159)
- On the singularity probability of discrete random matrices (2009) (157)
- On the equation DIV Y = f and applications to control of phases (2002) (156)
- Double recurrence and almost sure convergence. (1990) (153)
- On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE (1996) (148)
- The influence of variables in product spaces (1992) (145)
- On the Cauchy problem for the Kadomstev-Petviashvili equation (1993) (139)
- New Banach space properties of the disc algebra andH∞ (1984) (138)
- New estimates for elliptic equations and Hodge type systems (2007) (136)
- On wellposedness of the Zakharov system (1996) (135)
- On the Erdős-Volkmann and Katz-Tao ring conjectures (2003) (133)
- On dentability and the Bishop-Phelps property (1977) (132)
- Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces (2013) (131)
- On Exponential Sums in Finite Fields (2010) (127)
- Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces (2011) (124)
- Construction of blowup solutions for the nonlinear Schr ? odinger equation with critical nonlineari (1997) (123)
- A szemerédi type theorem for sets of positive density inRk (1986) (123)
- Toward a unified theory of sparse dimensionality reduction in Euclidean space (2013) (120)
- H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg–Landau equation (2004) (120)
- Generalization of Selberg's 3/16 Theorem and Affine Sieve (2009) (119)
- On the distribution of the fourier spectrum of Boolean functions (2002) (118)
- Limited Operators and Strict Cosingularity (1984) (118)
- On the equation = and application to control of phases (2002) (117)
- On the Hausdorff dimension of harmonic measure in higher dimension (1987) (115)
- Roth’s theorem on progressions revisited (2008) (115)
- On the Dimension of Kakeya Sets and Related Maximal Inequalities (1999) (115)
- On a variant of sum-product estimates and explicit exponential sum bounds in prime fields (2009) (114)
- On the Schrödinger maximal function in higher dimension (2012) (114)
- On the pointwise ergodic theorem onLp for arithmetic sets (1988) (113)
- Bounded orthogonal systems and the Λ(p)-set problem (1989) (112)
- Exponential sums and nonlinear Schrödinger equations (1993) (112)
- On Melnikov’s persistency problem (1997) (112)
- A class of specialLα spaces (1980) (111)
- On type of metric spaces (1986) (109)
- On a problem of Kadison and Singer. (1991) (109)
- Absolutely continuous spectrum for 1D quasiperiodic operators (2002) (107)
- On Λ(p)-subsets of squares (1989) (107)
- 4. Some New Estimates on Oscillatory Integrals (1995) (107)
- New estimates for the Laplacian, the div-curl, and related Hodge systems (2004) (106)
- Invariant measures for the2D-defocusing nonlinear Schrödinger equation (1996) (106)
- On the Distribution of Free Path Lengths¶for the Periodic Lorentz Gas (1998) (105)
- The discretized sum-product and projection theorems (2010) (105)
- Mordell's exponential sum estimate revisited (2005) (104)
- On growth of sobolev norms in linear schrödinger equations with smooth time dependent potential (1999) (104)
- A Spectral Gap Theorem in $SU(d)$ (2011) (104)
- Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus (2011) (102)
- Growth of Sobolev Norms in Linear Schrödinger Equations with Quasi-Periodic Potential (1999) (100)
- Anderson localization for Schrödinger operators on Z2 with quasi-periodic potential (2002) (100)
- Multilinear Exponential Sums in Prime Fields Under Optimal Entropy Condition on the Sources (2009) (98)
- Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order (2003) (98)
- Anderson Localization for Schrödinger Operators on ℤ with Potentials Given by the Skew–Shift (2001) (97)
- Disjointness of Moebius from Horocycle Flows (2013) (96)
- Scattering in the energy space and below for 3D NLS (1998) (95)
- A new characterization of Sobolev spaces (2006) (93)
- A note on the Schrödinger maximal function (2016) (92)
- Estimates for Cone Multipliers (1995) (92)
- On the Construction of Affine Extractors (2007) (87)
- An approach to pointwise ergodic theorems (1988) (87)
- Decouplings for curves and hypersurfaces with nonzero Gaussian curvature (2014) (86)
- On the Busemann-Petty problem for perturbations of the ball (1991) (85)
- On invariant tori of full dimension for 1D periodic NLS (2005) (84)
- Entropy of Quantum Limits (2003) (84)
- Hausdorff dimension and distance sets (1994) (83)
- Extension of a result of Benedek, Calderón and Panzone (1984) (82)
- Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: The 2D case (2013) (82)
- On diffusion in high-dimensional Hamiltonian systems and PDE (2000) (79)
- On the Cauchy and invariant measure problem for the periodic Zakharov system (1994) (79)
- A remark on Schrödinger operators (1992) (78)
- On the spectral type of Ornstein's class one transformations (1993) (78)
- Almost sure convergence and bounded entropy (1988) (77)
- Strong illposedness of the incompressible Euler equation in integer Cm spaces (2014) (77)
- Zaremba’s conjecture (2011) (77)
- Expansion in SLd(Z/qZ), q arbitrary (2010) (75)
- Invariant measures for the Gross-Piatevskii equation (1997) (75)
- An Improved Estimate in the Restricted Isometry Problem (2014) (74)
- Influences of Variables and Threshold Intervals under Group Symmetries (1997) (74)
- A Tribute to Paul Erdős: On arithmetic progressions in sums of sets of integers (1990) (72)
- Quasi-periodic solutions of nonlinear random Schrödinger equations (2008) (72)
- On the spectrum of lattice Schrödinger operators with deterministic potential (2002) (71)
- Estimates on exponential sums related to the Diffie–Hellman Distributions (2005) (70)
- Expansion and random walks in SL_d(Z/p^n Z): II (2008) (70)
- Banach spaces with a unique unconditional basis, up to permutation (1985) (70)
- Applications of the theory of semi-embeddings to Banach space theory (1983) (69)
- On the duality problem for entropy numbers of operators (1989) (69)
- Spectral gaps without the pressure condition (2016) (68)
- On an endpoint Kato-Ponce inequality (2014) (68)
- On the compactness of the support of solutions of dispersive equations (1997) (67)
- A proof of the positive density conjecture for integer Apollonian circle packings (2010) (66)
- Martingales valued in certain subspaces ofL1 (1980) (66)
- A remark on Bohr's inequality (2004) (66)
- Mean square of zeta function, circle problem and divisor problem revisited (2017) (66)
- Lp-Estimates for oscillatory integrals in several variables (1991) (65)
- On the correlation of the Moebius functionwith rank-one systems (2013) (64)
- Eigenfunction bounds for the Laplacian on the n -torus (1993) (64)
- Bounds on the density of states for Schrödinger operators (2011) (62)
- Sumsets of reciprocals in prime fields and multilinear Kloosterman sums (2012) (62)
- Positivity and continuity of the Lyapounov exponent for shifts on Td with arbitrary frequency vector and real analytic potentiald with arbitrary frequency vector and real analytic potential (2005) (62)
- Fourier dimension and spectral gaps for hyperbolic surfaces (2017) (61)
- Quantum Recurrence of a Subspace and Operator-Valued Schur Functions (2013) (61)
- Problems in Hamiltonian PDE’S (2010) (60)
- Anderson Localization for Schrödinger Operators on ℤ with Strongly Mixing Potentials (2000) (60)
- On the Hidden Shifted Power Problem (2011) (60)
- On Kahane's ultraflat polynomials (2009) (60)
- A Hausdorff-Young inequality for B-convex Banach spaces (1982) (59)
- Restriction of toral eigenfunctions to hypersurfaces and nodal sets (2011) (59)
- Anderson Localization for Quasi-Periodic Lattice Schrödinger Operators on $${\mathbb{Z}}^{d}$$ , d Arbitrary (2007) (58)
- On the size of k-fold sum and product sets of integers (2003) (58)
- On the structure of the Sobolev space H1/2 with values into the circle (2000) (58)
- A remark on normal forms and the “I-method” for periodic NLS (2004) (58)
- On the Morse-Sard Property and Level Sets of Sobolev and BV Functions (2010) (58)
- Sector Estimates for Hyperbolic Isometries (2010) (58)
- Remarks on the extension of lipschitz maps defined on discrete sets and uniform homeomorphisms (1987) (57)
- Minkowski sums and symmetrizations (1988) (57)
- Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball (2013) (57)
- On separable Banach spaces, universal for all separable reflexive spaces (1980) (56)
- The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization (1988) (56)
- $H^{∞}$ is a Grothendieck space (1983) (56)
- An ordinal LP-index for Banach spaces, with application to complemented subspaces of LP (1981) (55)
- Random Points in Isotropic Convex Sets (1998) (55)
- Real isomorphic complex Banach spaces need not be complex isomorphic (1986) (55)
- Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations (2004) (54)
- Lifting, degree, and distributional Jacobian revisited (2005) (54)
- Distribution of points on spheres and approximation by zonotopes (1988) (53)
- Estimates on Green’s functions, localization and the quantum kicked rotor model (2002) (53)
- Aspects of long time behaviour of solutions of nonlinear Hamiltonian evolution equations (1995) (52)
- Invariant Measures for NLS in Infinite Volume (2000) (52)
- Hölder Regularity of Integrated Density of States for the Almost Mathieu Operator in a Perturbative Regime (2000) (52)
- On the global Cauchy problem for the nonlinear Schrödinger equation (2002) (52)
- On hilbertian subsets of finite metric spaces (1986) (51)
- Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm (2010) (51)
- Estimation of certain exponential sums arising in complexity theory (2005) (51)
- On the Dunford-Pettis property (1981) (49)
- On the local-global conjecture for integral Apollonian gaskets (2012) (49)
- A Problem on Sums of Two Squares (2014) (49)
- Sieving and expanders (2006) (49)
- A construction of ℒ∞-spaces and related Banach spacesand related Banach spaces (1983) (48)
- Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat (2011) (48)
- A remark on the uncertainty principle for Hilbertian basis (1988) (48)
- On the radial variation of bounded analytic functions on the disc (1993) (48)
- On the Divisibility of Fermat Quotients (2010) (48)
- Dunford-pettis operators onL1 and the Radon-Nikodym property (1980) (47)
- On Pleijel's Nodal Domain Theorem (2013) (47)
- New classes of L[p]-spaces (1981) (47)
- Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve (2011) (47)
- Symmetrization and Isotropic Constants of Convex Bodies (2004) (46)
- An Approach to Wegner’s Estimate Using Subharmonicity (2009) (46)
- On the similarity problem for polynomially bounded operators on hilbert space (1986) (46)
- Random Lattice Schrödinger Operators with Decaying Potential: Some Higher Dimensional Phenomena (2003) (46)
- On representations of integers in thin subgroups of SL(2,Z) (2010) (45)
- New Classes of Lp Spaces (1981) (44)
- On a generalization of the Busemann-Petty problem (1998) (44)
- Analysis at Urbana: A remark on the maximal function associated to an analytic vector field (1989) (44)
- A counterexample to a complementation problem (1981) (44)
- On congruences with products of variables from short intervals and applications (2012) (44)
- On The Cauchy Problem for Periodic KDV-Type Equations (2020) (43)
- On the nodal sets of toral eigenfunctions (2010) (43)
- Appendix on return-time sequences (1989) (43)
- On the restriction and multiplier problems in R3 (1991) (42)
- Estimates related to steiner symmetrizations (1989) (42)
- Martingale transforms and complex uniform convexity (1986) (42)
- Chapter 1. On Strichartz’s Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori (2009) (42)
- On the Hardy-Littlewood maximal function for the cube (2012) (42)
- Markoff Triples and Strong Approximation (2015) (40)
- Dentability and finite-dimensional decompositions (1980) (40)
- On the Vinogradov mean value (2016) (39)
- Distjointness of Mobius from horocycle flows (2011) (39)
- An averaging result forl1-sequences and applications to weakly conditionally compact sets inLx1 (1979) (38)
- Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions (2016) (38)
- Vector-valued hausdorff-young inequalities and applications (1988) (38)
- A new function space and applications (2015) (38)
- On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus (2010) (37)
- Ruzsa’s problem on sets of recurrence (1987) (37)
- Prescribing the binary digits of primes (2011) (37)
- On toral eigenfunctions and the random wave model (2013) (37)
- Approximation of solutions of the cubic nonlinear Schrödinger equations by finite-dimensional equations and nonsqueezing properties (1994) (36)
- On diffusion in high-dimensional Hamiltonian systems (2005) (36)
- Local Statistics of Lattice Points on the Sphere (2012) (36)
- On convering a set in R N by balls of the same diameter (1991) (36)
- Anderson Localization for Time Quasi-Periodic Random Schrödinger and Wave Equations (2004) (36)
- Bilinear forms on ^{∞} and bounded bianalytic functions (1984) (36)
- Sidon sets and Riesz products (1985) (36)
- Some effective results for ×a×b (2009) (35)
- Anderson localization for the band model (2000) (35)
- A Gauss sum estimate in arbitrary finite fields (2006) (35)
- Mean value estimates for Weyl sums in two dimensions (2015) (35)
- The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces (1984) (35)
- Control for Schrödinger operators on 2-tori: rough potentials (2013) (34)
- A study guide for the l2 decoupling theorem (2016) (34)
- A remark on gradients of harmonic functions in dimension ≥3 (1990) (34)
- On the Isotropy-Constant Problem for “PSI-2”-Bodies (2003) (33)
- Prescribing the binary digits of primes, II (2013) (33)
- Exponential sum estimates over a subgroup in an arbitrary finite field (2011) (33)
- On Representations of Integers in Thin Subgroups of $${{\rm SL}_2({\mathbb {Z}})}$$ (2010) (33)
- Improved estimates for the discrete Fourier restriction to the higher dimensional sphere (2012) (33)
- Exponential sum estimates over subgroups and almost subgroups of $$ \mathbb{Z}_{Q}^{*} $$, where Q is composite with few prime factors (2006) (32)
- A problem of Douglas and Rudin on factorization (1986) (32)
- On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn (2015) (32)
- On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds (2012) (31)
- A nonlinear version of Roth's theorem for sets of positive density in the real line (1988) (31)
- BMO‐Type Norms Related to the Perimeter of Sets (2014) (31)
- Invariant measures and stiffness for non-Abelian groups of toral automorphisms⁎ (2007) (30)
- Expanders and dimensional expansion (2009) (30)
- Recent progress on quasi-periodic lattice Schrödinger operators and Hamiltonian PDEs (2004) (30)
- Subspaces of L N ∞ , arithmetical diameter and sidon sets (1985) (30)
- On the Approximation Properties for the Space H (1985) (29)
- On the Approximation Properties for the Space H (1985) (29)
- Exponential sum estimates over subgroups ofZ*q,q arbitrary,q arbitrary (2005) (29)
- On the spectrum of lattice schrödinger operators with deterministic potential (II) (2002) (29)
- On theLp-bounds for maximal functions associated to convex bodies inRn (1986) (29)
- A quantitative Oppenheim theorem for generic diagonal quadratic forms (2016) (29)
- On the Approximation Properties for the Space H (1985) (29)
- Breaking the k2 barrier for explicit RIP matrices (2011) (28)
- A new estimate for the topological degree (2005) (28)
- On Lp-Resolvent Estimates and the Density of Eigenvalues for Compact Riemannian Manifolds (2012) (27)
- Some consequences of Pisier’s approach to interpolation (1992) (26)
- EXPONENTIAL SUM ESTIMATES OVER SUBGROUPS AND ALMOST SUBGROUPS OF Zq, WHERE q IS COMPOSITE WITH FEW PRIME FACTORS (2006) (26)
- Limit behaviour of large Frobenius numbers (2007) (26)
- New Bounds for the Discrete Fourier Restriction to the Sphere in 4D and 5D (2014) (26)
- A study guide for the $l^2$ Decoupling Theorem (2016) (26)
- Approximating the ball by a minkowski sum of segments with equal length (1993) (26)
- New bounds on exponential sums related to the Diffie–Hellman distributions (2004) (26)
- Some results on non-linear recurrence (1994) (25)
- Multiplicative congruences with variables from short intervals (2012) (24)
- Estimates related to sumfree subsets of sets of integers (1997) (24)
- On random Schrödinger operators on $\mathbb Z^2$ (2001) (24)
- Distances between normed spaces, their subspaces and quotient spaces (1986) (23)
- has no equivalent strictly convex norm (1980) (23)
- On Martingales Transforms in Finite Dimensional Lattices with an Appendix on the K‐Convexity Constant (1984) (23)
- EXPANSION IN SL 2 ( R ) AND MONOTONE EXPANDERS (2013) (23)
- Geometry of finite dimensional subspaces and quotients of Lp (1989) (23)
- Chapter 5 - Λ P-sets in Analysis: Results, Problems and Related Aspects (2001) (23)
- Restriction of toral eigenfunctions to hypersurfaces (2009) (23)
- On the correlation of the Moebius function with random rank-one systems (2011) (22)
- Gamburd A spectral gap theorem in SU ( d ) (2012) (22)
- On dimension free maximal inequalities for convex symmetric bodies in ℜn (1987) (22)
- Additive Patterns in Multiplicative Subgroups (2014) (22)
- On a geometric inequality (1988) (22)
- Strongly exposed points in weakly compact convex sets in Banach spaces (1976) (22)
- Spatial statistics for lattice points on the sphere I: Individual results (2016) (22)
- The non-isomorphism of H1-spaces in one and several variables (1982) (21)
- On the behavior of the constant in the littlewood-paley inequality (1989) (21)
- The sum-product theorem in ℤq with q arbitrary (2008) (21)
- On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in ℝD (1997) (21)
- Decoupling inequalities and some mean-value theorems (2014) (20)
- Anderson localization for two interacting quasiperiodic particles (2018) (20)
- A modular Szemeredi-Trotter theorem for hyperbolas (2012) (20)
- Spherical summation and uniqueness of multiple trigonometric series (1996) (20)
- A characterization of non-dunford-pettis operators onL1 (1980) (19)
- Exponential sum estimates in finite commutative rings and applications (2007) (19)
- On Localization for Lattice Schrödinger Operators Involving Bernoulli Variables (2004) (19)
- Translation invariant forms on $L^p(G)(1 (1986) (18)
- Character sums and deterministic polynomial root finding in finite fields (2013) (18)
- The Affine Sieve Beyond Expansion I: Thin Hypotenuses (2013) (18)
- Expansion in SL 2$${(\mathbb{R})}$$ and monotone expanders (2013) (18)
- Applications of the spaces of homogeneous polynomials to some problems on the ball algebra (1985) (18)
- New results on expanders (2006) (18)
- Walsh subspaces of $L^p$-product spaces (1980) (17)
- A Remark on Quantum Ergodicity for CAT Maps (2007) (17)
- Spectral gaps in SU(d) (2010) (17)
- Small gaps in the spectrum of the rectangular billiard (2016) (17)
- Corrigenda to: Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings and Fixed Points of the Discrete Logarithm (2009) (17)
- On the Distribution of Dirichlet Sums (1993) (17)
- Kloosterman sums in residue rings (2013) (17)
- Sidonicity and variants of Kaczmarz's problem (2015) (17)
- On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder (2011) (17)
- l ∞ /c 0 has no Equivalent Strictly Convex Norm (1980) (17)
- Almost euclidean sections in spaces with a symmetric basis (1989) (17)
- Construction of sets of positive measure not containing an affine image of a given infinite structure (1987) (17)
- Distribution of Elements of Cosets of Small Subgroups and Applications (2011) (16)
- Markoff Surfaces and Strong Approximation: 1 (2016) (16)
- On the Strong Density Conjecture for Integral Apollonian Circle Packings (2012) (16)
- On kolmogorov's rearrangement problem for orthogonal systems and garsia's conjecture (1989) (16)
- Appendix to ‘Roth’s theorem on progressions revisited,’ by (2008) (16)
- Nonlinear Roth type theorems in finite fields (2016) (15)
- A remark on entropy of Abelian groups and the invariant uniform approximation property (1987) (15)
- On large values estimates for Dirichlet polynomials and the density hypothesis for the Riemann zeta function (2000) (15)
- Embedding L 1 in L 1 /H 1 (1983) (15)
- Beyond Expansion II: Low-Lying Fundamental Geodesics (2014) (15)
- Analysis at Urbana: Restricted invertibility of matrices and applications (1989) (15)
- Decouplings for surfaces in R^4 (2015) (15)
- Positive lyapounov exponents for most energies (2000) (15)
- A reduction of the slicing problem to finite volume ratio bodies (2003) (14)
- On the distribution of the residues of small multiplicative subgroups of $$ \mathbb{F}_p $$ (2009) (14)
- On the smallest pseudopower (2009) (14)
- On finitely generated closed ideals in $H^\infty (D)$ (1985) (14)
- W1,p estimates for solutions to the Ginzburg–Landau equation with boundary data in H1/2 (2001) (14)
- Dimension-Free Estimates for Discrete Hardy-Littlewood Averaging Operators Over the Cubes in ℤd (2019) (14)
- Gibbs Measures and Quasi-Periodic Solutions for Nonlinear Hamiltonian Partial Differential Equations (1996) (14)
- On the almost everywhere convergence of ergodic averages for power-bounded operators on LP-subspaces (1991) (14)
- On a Homogenization Problem (2017) (14)
- Nodal intersections and Lp restriction theorems on the torus (2013) (14)
- Integral Apollonian circle packings and prime curvatures (2011) (13)
- Expansion and random walks in $\mathrm {SL}_d(\mathbb {Z}/p^n\mathbb {Z})$: I (2008) (13)
- Restrictions from $ℝ^{n}$ to $ℤ^{n}$ of weak type (1,1) multipliers (1994) (13)
- Harmonic Analysis and Nonlinear Partial Differential Equations (1995) (13)
- New bounds for the discrete Fourier restriction to the sphere in four and five dimensions (2013) (13)
- Canonical Sobolev projections of weak type (1,1) (2001) (13)
- On Long-Time Behaviour of Solutions of Linear Schrödinger Equations with Smooth Time-Dependent Potential (2003) (13)
- Roots of Polynomials in Subgroups of and Applications to Congruences (2008) (12)
- Decimations of l-Sequences and Permutations of Even Residues mod p (2009) (12)
- Some Diophantine applications of the theory of group expansion (2013) (12)
- On Dimension-Free Variational Inequalities for Averaging Operators in $${\mathbb{R}^d}$$Rd (2017) (12)
- Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball (2012) (12)
- Complements to the paper "Lifting, degree, and the Distributional Jacobian Revisited" (2004) (12)
- Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces (2014) (12)
- On finite dimensional homogeneous Banach spaces (1988) (12)
- Strong Ill-Posedness of the 3D Incompressible Euler Equation in Borderline Spaces (2019) (12)
- (1) Limiting Embedding Theorems for W 8,p When S 1" 1 and Applications (12)
- Remarks on Montgomery's conjectures on dirichlet sums (1991) (12)
- Decoupling for Perturbed Cones and the Mean Square of | ζ ( 12 + it ) | (2017) (12)
- Decoupling for perturbed cones and mean square of $|\zeta(\frac 12+it)|$ (2015) (11)
- On the Fourier-Walsh spectrum of the Moebius function (2011) (11)
- On the parity of k-th powers modulo p. A generalization of a problem of Lehmer (2011) (11)
- Homogeneous polynomials on the ball and polynomial bases (1989) (11)
- Uniqueness and free interpolation for logarithmic potentials and the cauchy problem for the laplace equation in 529-1529-1529-1 (1995) (11)
- Some Arithmetical Applications of the Sum-Product Theorems in Finite Fields (2007) (11)
- Sum–product theorems and exponential sum bounds in residue classes for general modulus (2007) (11)
- Sets with the Radon-Nikodým property in conjugate Banach space (1980) (11)
- Sum-Product Theorems and Applications (2010) (11)
- On bases in the disc algebra (1984) (11)
- On the primarity ofH∞-spaces (1983) (11)
- Problems of almost everywhere convergence related to harmonic analysis and number theory (1990) (10)
- W^{1,p} estimates for solutions to the Ginzburg-Landau equation with boundary data in H^{1/2}. (2001) (10)
- Estimates on polynomial exponential sums (2010) (10)
- The dimension conjecture for polydisc algebras (1984) (10)
- One cannot hear the winding number (2006) (10)
- On a multilinear character sum of Burgess (2010) (10)
- Distribution of consecutive modular roots of an integer (2008) (9)
- Embedding $L\sp{1}$ in $L\sp{1}/H\sp{1}$ (1983) (9)
- Galilean Boost and Non-uniform Continuity for Incompressible Euler (2019) (9)
- On quasi-periodic lattice Schrödinger operators (2003) (9)
- Beyond Expansion II: Traces of Thin Semigroups (2013) (9)
- Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation (2009) (9)
- Decouplings for Real Analytic Surfaces of Revolution (2019) (9)
- Sum-product theorem and exponential sum estimates in residue classes with modulus involving few prime factors (2004) (9)
- A geometric characterization of the Radon-Nikodym property in Banach spaces (1978) (9)
- A Remark on Solutions of the Pell Equation (2013) (9)
- Nonlinear Roth type theorems in finite fields (2017) (9)
- Bounds on oscillatory integral operators (2011) (8)
- Nonlinear Schrödinger equation with a random potential (2006) (8)
- On lattice packing of convex symmetric sets in ℜn (1987) (8)
- Anderson—Bernoulli Models (2005) (8)
- Thermodynamic expansion to arbitrary moduli (2015) (8)
- UNIFORM CONGRUENCE COUNTING FOR SCHOTTKY SEMIGROUPS (2016) (8)
- Finitely Supported Measures on S{L}_{2}(\mathbb{R}) Which are Absolutely Continuous at Infinity (2012) (8)
- Return times of dynamical systems (1989) (8)
- An application of group expansion to the Anderson-Bernoulli model (2013) (8)
- Perimeter of sets and BMO-type norms (2014) (7)
- On Sharp Thresholds of Monotone Properties (1997) (7)
- On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective (2018) (7)
- A new class ofℒ1-spaces (1981) (7)
- Partial quotients and representation of rational numbers (2012) (7)
- Toward a unified theory of sparse dimensionality reduction in Euclidean space (2015) (7)
- Monotone Boolean functions capture their primes (2012) (7)
- $l^p$ decouplings for hypersurfaces with nonzero Gaussian curvature (2014) (7)
- On a paper of Erdös and Szekeres (2015) (7)
- Estimates of bernstein widths of sobolev spaces (1989) (6)
- Bounded variation of measure convolutions (1993) (6)
- Erratum to: On Representations of Integers in Thin Subgroups of $${{\rm {SL}}_2(\mathbb {Z})}$$ (2010) (6)
- On Representation of Integers by Binary Quadratic Forms (2011) (6)
- On the Morse-Sard property and level sets of $W^{n,1}$ Sobolev functions on ${\mathbb R}^n$ (2012) (6)
- Sum-product theorems in algebraic number fields (2009) (6)
- On pair correlation for generic diagonal forms (2016) (6)
- A Lower Bound for the Lyapounov Exponents of the Random Schrödinger Operator on a Strip (2013) (6)
- The Essential Centre of the mod a Diagonalization Ideal Commutant of an n-tuple of Commuting Hermitian Operators (2013) (6)
- Monotone expansion (2011) (6)
- On multiple sum and product sets of finite sets of integers (2003) (5)
- ON FINITELY GENERATED CLOSED IDEALS IN H ° ° ( D ) (2017) (5)
- A remark on the behaviour ofLp-multipliers and the range of operators acting onLp-spaces (1992) (5)
- Remarks on Halasz-Montgomery Type Inequalities (1995) (5)
- On Trigonometric Series in Super Reflexive Spaces (1981) (5)
- A result on the isomorphic embeddability of l¹(Γ) (1984) (5)
- Chapter 20. Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations (2005) (5)
- Ju n 20 10 Expansion in SL d ( Z / q Z ) , q arbitrary (2021) (5)
- On a Problem of Farrell and Vershynin in Random Matrix Theory (2017) (5)
- Mordell type exponential sum estimates in fields of prime order (2004) (5)
- Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential (1999) (5)
- Threshold Intervals under Group Symmetries (1998) (5)
- On the correlation of the Moebius functionwith rank-one systems (2013) (5)
- Affine extractors over large fields with exponential error (2014) (5)
- A Note on Lyapunov Exponents of Deterministic Strongly Mixing Potentials (2013) (4)
- Complements of subspaces of ℓ p n ; p ≥1 which are uniquely determined (1987) (4)
- Borel sets with $F_σδ$-section (1980) (4)
- A remark on finite-dimensional $P_{λ}$-spaces (1982) (4)
- On Eigenvalue spacings for the 1-D Anderson model with singular site distribution (2013) (4)
- New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography (2005) (4)
- A Remark on a Maximal Operator for Fourier Multipliers (2000) (4)
- On the Lyapounov Exponents of Schrödinger Operators Associated with the Standard Map (2012) (4)
- On an exponential sum related to the Diffie-Hellman cryptosystem (2006) (4)
- Beyond expansion, III: Reciprocal geodesics (2016) (4)
- Optimal mean value estimates for the quadratic Weyl sums in two dimensions (2015) (4)
- On Discrete Hardy–Littlewood Maximal Functions over the Balls in $${\boldsymbol {\mathbb {Z}^d}}$$ : Dimension-Free Estimates (2020) (4)
- On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates (2018) (4)
- The Cauchy problem for nonlinear Schrödinger equation (NLS) with critical nonlinearity (1997) (3)
- On the minimum norm of representatives of residue classes in number fields (2007) (3)
- Walsh subspaces of Lp-product spaces (2018) (3)
- Embeddinglpk in subspaces ofLp forp>2 (1990) (3)
- New classes of ℒ ∞ $${\mathcal{L}^\infty }$$-Spaces (1981) (3)
- l1 Sequences Generated by Sidon Sets (1984) (3)
- Influential coalitions for Boolean Functions (2014) (3)
- Control for Schr\"odinger equations on 2-tori: rough potentials (2013) (3)
- HAMILTONIAN METHODS IN NONLINEAR EVOLUTION EQUATIONS (1997) (3)
- On uniformly bounded bases in spaces of holomorphic functions (2016) (3)
- Some remarks on the Banach space structure of the ball-algebras (1985) (3)
- On the Local Eigenvalue Spacings for Certain Anderson-Bernoulli Hamiltonians (2013) (3)
- On the Control Problem for Schrödinger Operators on Tori (2014) (3)
- Translation invariant complemented subspaces of $L^{p}$ (1982) (3)
- On a multi-parameter variant of the Bellow-Furstenberg problem (2022) (3)
- Periodic Nonlinear Schrδdinger Equation (1994) (3)
- New developments in combinatorial number theory and applications (2010) (3)
- A nondentable set without the tree property (1980) (2)
- Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $\mathbb Z^d$ (2018) (2)
- Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) (2009) (2)
- Chapter Three On Oscillatory Integral Operators in Higher Dimensions (2014) (2)
- On Random Walks in Large Compact Lie Groups (2015) (2)
- Quasi-periodic solutions of nonlinear random Schr\"odinger equations (2008) (2)
- Prescribing the binary digits of primes (2012) (2)
- Three Applications of the Siegel Mass Formula (2018) (2)
- On a paper of Erd\"os and Szekeres (2015) (2)
- Random walks and expansion in SLd(Z/pnZ) (2008) (2)
- $F_σδ$-section of Borel sets (1980) (2)
- On the uniform approximation of the partial sum of the Dirichlet series by a shorter sum (2010) (2)
- CORRECTIONS AND ADDITIONS TO “ENTROPY OF QUANTUM LIMITS” JEAN BOURGAIN AND ELON LINDENSTRAUSS (2004) (2)
- A class of ℒ 1 -Spaces (1981) (1)
- Around the Sum-product Phenomenon (2013) (1)
- On uniformly bounded basis in spaces of holomorphic functions (2015) (1)
- A density condition for analyticity of the restriction algebra (1987) (1)
- On the Schrödinger maximal function in higher dimension (2013) (1)
- Decomposition in the product of a measure space and a Polish space (1979) (1)
- Anderson localization for two interacting quasiperiodic particles (2019) (1)
- An overview of results on the Cauchy problem for NLS (1999) (1)
- A Finitary Hasse Principle for Diagonal Curves (2014) (1)
- N T ] 5 O ct 2 01 1 DISJOINTNESS OF MOBIUS FROM HOROCYCLE FLOWS (2013) (1)
- Convergence of ergodic averages on lattice random walks (1993) (1)
- Bounds on the density of states for Schrödinger operators (2012) (1)
- A direct proof of van der Vaart's theorem (1986) (1)
- A prime number theorem for the majority function (2012) (1)
- On the dichotomy problem for tensor algebras (1986) (1)
- Quasi-periodic Solutions of Hamiltonian Evolution Equations (2020) (1)
- On the Fourier-Walsh spectrum of the Moebius function, II (2016) (1)
- Partial Differential Equations Restriction of toral eigenfunctions to hypersurfaces (2009) (0)
- Breaking the k 2 Barrier for Explicit RIP Matrices (Extended Abstract) (2011) (0)
- On toral eigenfunctions and the random wave model (2014) (0)
- Prescribin the binary digits of the primes, II (2013) (0)
- Chapter 13. Point Spectrum in Multifrequency Models at Small Disorder (2005) (0)
- On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder (2012) (0)
- Decouplings for curves and hypersurfaces with nonzero Gaussian curvature (2017) (0)
- Additive Patterns in Multiplicative Subgroups (2014) (0)
- Multiplicative congruences with variables from short intervals (2014) (0)
- Chapter 17. Quasi-Periodic Localization on the Zd-lattice (d > 1) (2005) (0)
- Nonlinear Schrödinger equation with periodic boundary conditions (1999) (0)
- On quadratic irrationals with bounded partial quotients (2018) (0)
- On Lp-Resolvent Estimates and the Density of Eigenvalues for Compact Riemannian Manifolds (2014) (0)
- A quantitative Oppenheim theorem for generic diagonal quadratic forms (2016) (0)
- A New Approach to Spectral Gap Problems (2006) (0)
- Chapter 15. Application to Jacobi Matrices Associated with Skew Shifts (2005) (0)
- On the Hardy-Littlewood maximal function for the cube (2014) (0)
- Chapter 9. Some Facts about Semialgebraic Sets (2005) (0)
- Uniform approximation of partial sums of a Dirichlet series by shorter sums and Φ-widths (2012) (0)
- On a theorem of Friedlander and Iwaniec (2010) (0)
- A note on the Schrödinger maximal function (2016) (0)
- Mathematical Analysis A new characterization of Sobolev spaces (2006) (0)
- A class of ℒ 1 $${\mathcal{L}^1}$$-Spaces (1981) (0)
- Decoupling inequalities and some mean-value theorems (2017) (0)
- Affine extractors over large fields with exponential error (2015) (0)
- A Lower Bound for the Lyapounov Exponents of the Random Schrödinger Operator on a Strip (2013) (0)
- Joran Lindenstrauss, in Memoriam (2015) (0)
- On congruences with products of variables from short intervals and applications (2013) (0)
- COMPUTATIONAL INTRACTABILITY AND PSEUDORANDOMNESS The areas of computational intractability and pseudorandomness (2010) (0)
- Global wellposedness below energy norm (1999) (0)
- Analysis in functional spaces (1984) (0)
- On a paper of Erdös and Szekeres (2018) (0)
- Fourier dimension and spectral gaps for hyperbolic surfaces (2017) (0)
- Chapter 10. Localization (2005) (0)
- A class of \({\mathcal{L}^1}\)-Spaces (1981) (0)
- On the global Cauchy probl Schrodinger equation (2016) (0)
- Expansion in SLd(Z/qZ), q arbitrary (2011) (0)
- Chapter 3. Herman’s Subharmonicity Method (2005) (0)
- Chapter 11. Generalization to Certain Long-Range Models (2005) (0)
- N T ] 5 D ec 2 01 1 ON THE CORRELATION OF THE MOEBIUS FUNCTION WITH RANK-ONE SYSTEMS (2011) (0)
- Restriction of toral eigenfunctions to hypersurfaces and nodal sets (2012) (0)
- Chapter 8. Refinements (2005) (0)
- Chapter 16. Application to the Kicked Rotor Problem (2005) (0)
- Quantum Recurrence of a Subspace and Operator-Valued Schur Functions (2014) (0)
- Chapter 14. A Matrix-Valued Cartan-Type Theorem (2005) (0)
- On the number of $k$th powers inside arithmetic progressions (2018) (0)
- Corrigendum to “Apollonian Circle Packings and Prime Curvatures” (2013) (0)
- Chapter 5. LDT for Shift Model (2005) (0)
- Some results on the bidisc algebra (2019) (0)
- Chapter 19. Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations (2005) (0)
- On a Homogenization Problem (2018) (0)
- ON ONE RESULT OF J.BOURGAIN (2010) (0)
- On the Vinogradov mean value (2017) (0)
- Nodal intersections and Lp restriction theorems on the torus (2015) (0)
- ON SEPARABLE BANACH SPACES , UNIVERSAL FOR ALL SEPARABLE REFLEXD (2010) (0)
- Monotone Boolean functions capture their primes (2014) (0)
- New Classes of ℒ p $${\mathcal{L}^p}$$ -Spaces (1981) (0)
- On the Fourier-Walsh spectrum of the Moebius function, II (2016) (0)
- Chapter 12. Lyapounov Exponent and Spectrum (2005) (0)
- Corrigendum to “Apollonian Circle Packings and Prime Curvatures” (2013) (0)
- THE ERGODIZATION TIME FOR LINEAR FLOWS ON TORI ; APPLICATIONS TO KINETIC THEORY (2021) (0)
- ON SEPARABLE BANACH SPACES, UNIVERSAL FOR ALL (2010) (0)
- GIBBS MEASURE EVOLUTION IN RADIAL NONLINEAR WAVE AND SCHR ¨ ODINGER EQUATIONS ON THE BALL MESURES DE GIBBS ET ´ EQUATIONS NON-LIN ´ EAIRES DES ONDES ET SCHR ¨ ODINGER SUR LA BOULE (2012) (0)
- Moebius Schrodinger (2010) (0)
- Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat (2013) (0)
- A stabilization property and its applications in theory of sections (1977) (0)
- Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces (2012) (0)
- Additive Patterns in Multiplicative Subgroups Noga Alon (2014) (0)
- Prescribing the binary digits of primes, II (2014) (0)
- Chapter 6. Avalanche Principle in SL2(R) (2005) (0)
- Nonlinear Roth type theorems in finite fields (2017) (0)
- Chapter 18. An Approach to Melnikov’s Theorem on Persistency of Nonresonant Lower Dimension Tori (2005) (0)
- Integral Apollonian circle packings and prime curvatures (2012) (0)
- On the Fourier-Walsh spectrum of the Moebius function (2013) (0)
- Chapter 2. Transfer Matrix and Lyapounov Exponent (2005) (0)
- Aleksander (Olek) Pelczynski (1932–2012) (2017) (0)
- A Harmonic Analysis Approach to Problems in Nonlinear Partial Differential Equations (1994) (0)
- Addendum: Discussions at the Dead Sea (2000) (0)
- On the local-global conjecture for integral Apollonian gaskets (2013) (0)
- On A Conjecture of Zaremba's (2011) (0)
- Galilean Boost and Non-uniform Continuity for Incompressible Euler (2019) (0)
- Anderson Localization for Time Quasi Periodic Random Sch\"odinger and Wave Operators (2002) (0)
- Strong illposedness of the incompressible Euler equation in integer Cm spaces (2015) (0)
- Chapter 7. Consequences for Lyapounov Exponent, IDS, and Green’s Function (2005) (0)
- Chapter 4. Estimates on Subharmonic Functions (2005) (0)
- A study guide for the l2 decoupling theorem (2017) (0)
- Incomplete Kloosterman sums and their applications (2016) (0)
- Geometrical implications of certain finite dimensional structures (1981) (0)
- An application of group expansion to the Anderson-Bernoulli model (2014) (0)
- On quadratic irrationals with bounded partial quotients (2013) (0)
- OURGAIN Sidon sets and Riesz products (2017) (0)

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