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作者：Defant, Andreas; Frerick, Leonhard; Ortega-Cerda, Joaquim; Ounaies, Myriam; Seip, Kristian
摘要：The Bohnenblust-Hille inequality says that the l(2m/m+1)-norm of the coefficients of an m-homogeneous polynomial P on C-n is bounded by parallel to P parallel to(infinity) times a constant independent of n, where parallel to.parallel to(infinity) denotes the supremum norm on the polydisc D-n. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be C-m for some C> 1. Combining this improved version of the Bohnenblust-Hille inequality with...
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作者：Vergne, Michele
摘要：The semi-discrete convolution with the box spline is an important tool in approximation theory. We give a formula for the difference between semi-discrete convolution and convolution with the box spline. This formula involves multiple Bernoulli polynomials.
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作者：Kovacs, Sandor J.; Lieblich, Max
摘要：We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is finite, and that this number is uniformly bounded in any finite type family of base varieties. As a corollary we show that a direct generalization of the geometric version of Shafarevich's original conjecture holds for infinitesimally rigid families of canonically polarized varieties.
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作者：Remling, Christian
摘要：I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrodinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme is the following: It is extremely difficult to produce absolutely continuous spectrum in one space d...
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作者：Chai, Ching-Li; Oort, Frans
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作者：Izzo, Alexander J.
摘要：It is shown that if A is a uniform algebra generated by a family (13 of complex-valued C-1 functions on a compact C-1 manifold-with-boundary M, the maximal ideal space of A is M, and E is the set of points where the differentials of the functions in Phi fail to span the complexified cotangent space to M, then A contains every continuous function on M that vanishes on E. This answers a 45-year-old question of Michael Freeman who proved the special case in which the manifold M is two-dimensional...
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作者：Bejenaru, I.; Ionescu, A. D.; Kenig, C. E.; Tataru, D.
摘要：We consider the Schrodinger map initial-value problem {partial derivative t phi - phi x Delta phi on R-d x R, phi(0) = phi(0) where phi: Rd x R -> R-2 hooked right arrow R-3 is a smooth function. In all dimensions d >= 2, we prove that the Schrodinger map initial-value problem admits a unique global smooth solution phi is an element of C (R : H-Q(infinity)), Q is an element of S-2 Q), Q 2 S 2, provided that the data phi(0) is an element of H-Q(infinity) is smooth and satisfies the smallness co...
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作者：Badziahin, Dzmitry; Pollington, Andrew; Velani, Sanju
摘要：For any i, j >= 0 with i + j = 1, let Bad(i, j) denote the set of points (x, y) is an element of R-2 for which max{parallel to qx parallel to(1/i), parallel to qy parallel to(1/j)} > c/q for all q is an element of N. Here c = c(x, y) is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.
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作者：Benoist, Yves; Quint, Jean-Francois
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作者：Sanders, Tom
摘要：We show that if A subset of {1,..., N} contains no nontrivial three-term arithmetic progressions then vertical bar A vertical bar = O(N/log(1-o(1)) N).
