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Another look at Sobolev spaces
The standard seminorm in the space $W^{s,p}$, with $s$<$1$, does not converge, when $s$ approaches $1$, to the corresponding $W^{1,p}$ seminorm. We prove that continuity is restored provided weExpand
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Periodic nonlinear Schrödinger equation and invariant measures
AbstractIn this paper we continue some investigations on the periodic NLSEiuu +iuxx +u|u|p-2 (p≦6) started in [LRS]. We prove that the equation is globally wellposed for a set of data Φ of fullExpand
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On lipschitz embedding of finite metric spaces in Hilbert space
It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space withExpand
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A sum-product estimate in finite fields, and applications
AbstractLet A be a subset of a finite field $$ F := \mathbf{Z}/q\mathbf{Z} $$ for some prime q. If $$ |F|^{\delta} < |A| < |F|^{1-\delta} $$ for some δ > 0, then we prove the estimate $$ |A + A| +Expand
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Green's Function Estimates for Lattice Schrödinger Operators and Applications.
Acknowledgment v CHAPTER 1: Introduction 1 CHAPTER 2: Transfer Matrix and Lyapounov Exponent 11 CHAPTER 3: Herman's Subharmonicity Method 15 CHAPTER 4: Estimates on Subharmonic Functions 19 CHAPTERExpand
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Bounds on Oscillatory Integral Operators Based on Multilinear Estimates
We apply the Bennett–Carbery–Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved Lp estimates in the SteinExpand
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