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1,255
ON THE RESTRICTION CONJECTURE
, 2002
"... We prove the restriction conjecture for the class of functions consisting of products of radial functions and spherical harmonics Y (ω), when Y (ω) is aproduct of (t) is an ultraspherical polynomial. factors of the form (sin ω) s−j P (s) n (cos(ω)) and P (s) ..."
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Cited by 1 (0 self)
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We prove the restriction conjecture for the class of functions consisting of products of radial functions and spherical harmonics Y (ω), when Y (ω) is aproduct of (t) is an ultraspherical polynomial. factors of the form (sin ω) s−j P (s) n (cos(ω)) and P (s)
SOME RECENT PROGRESS ON THE RESTRICTION CONJECTURE
, 2003
"... Abstract. We survey recent developments on the Restriction conjecture. ..."
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Cited by 21 (0 self)
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Abstract. We survey recent developments on the Restriction conjecture.
Slicing surfaces and fourier restriction conjecture
 arXiv:0804.3696, Proceedings of the Edinburgh Mathematical Society
"... Abstract. We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid, the elliptic hyperboloid in R n implies that for the cone in R n+1. We also prove a new restriction estimate for any surface in R 3 locally i ..."
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Cited by 1 (0 self)
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Abstract. We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid, the elliptic hyperboloid in R n implies that for the cone in R n+1. We also prove a new restriction estimate for any surface in R 3 locally
The BochnerRiesz Conjecture Implies The Restriction Conjecture
 363 – 375. MR 1666558 52
, 1999
"... ..."
A NOTE ON THE CONE RESTRICTION CONJECTURE IN THE CYLINDRICALLY SYMMETRIC CASE
, 2007
"... In this short note, we present two proofs showing that the classical linear adjoint cone restriction conjecture in R × R n holds for all cylindrically symmetric functions supported on the cone, where n ≥ 2. ..."
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Cited by 2 (0 self)
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In this short note, we present two proofs showing that the classical linear adjoint cone restriction conjecture in R × R n holds for all cylindrically symmetric functions supported on the cone, where n ≥ 2.
On the multilinear restriction and Kakeya conjectures
 ACTA MATH
, 2006
"... We prove dlinear analogues of the classical restriction and Kakeya conjectures in Rd. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians, closely related to heat flow. We conclude by giving some applications to the corresponding variable ..."
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Cited by 50 (11 self)
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We prove dlinear analogues of the classical restriction and Kakeya conjectures in Rd. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians, closely related to heat flow. We conclude by giving some applications to the corresponding
Bethe Ansatz for Quantum Strings
, 2004
"... We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by add ..."
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Cited by 281 (16 self)
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We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz
A bilinear approach to the restriction and Kakeya conjectures
 J. AMER. MATH. SOC
, 1998
"... Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the (L p, L p) spherical restriction theorem of Wolff [27] from p&g ..."
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Cited by 68 (24 self)
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Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the (L p, L p) spherical restriction theorem of Wolff [27] from p
ON SNEVILY’S CONJECTURE AND RESTRICTED SUMSETS
 J. COMBIN. THEORY SER. A 103(2003), NO.2, 288–301.
, 2003
"... Let G be an additive abelian group whose finite subgroups are all cyclic. Let A1,..., An (n> 1) be finite subsets of G with cardinality k> 0, and let b1,..., bn be pairwise distinct elements of G with odd order. We show that for every positive integer m � (k −1)/(n−1) there are more than (k − ..."
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Cited by 21 (14 self)
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− 1)n − (m + 1) ( n) sets {a1,..., an} such that a1 ∈ A1,..., an ∈ 2 An, and both ai ̸ = aj and mai + bi ̸ = maj + bj (or both mai ̸ = maj and ai + bi ̸ = aj + bj) for all 1 � i < j � n. This extends a recent result of Dasgupta, Károlyi, Serra and Szegedy on Snevily’s conjecture. Actually stronger
Results 1  10
of
1,255