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Interpolation of Operators
An Introduction to Sobolev Spaces and Pseudo
The Linear Schrodinger Equation
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argument assume asymptotic bicharacteristic flow bilinear estimate bounded Cauchy-Schwarz inequality Chapter coefficients Colliander Combining Consider the IVP constant contraction mapping Corollary 5.6 data uo decay deduce defined Definition denotes depends derivatives dispersive equations elliptic equation in 6.1 established example exercise extend Fourier transform G C(R G L^R G S(R G Z+ Galilean invariant given global result global well-posedness Hence Hilbert transform Hint hypothesis identity idtu inequality initial data integral equation 5.11 interval T,T IVP associated KdV equation Kenig Korteweg-de Vries equation L2 norm Lemma mKdV Moreover nonlinear Schrodinger equation nontrapping norm notation obtain oo oo oo proof of Theorem properties Proposition prove pseudo-differential operators Riesz potentials Riesz-Thorin Riesz-Thorin theorem satisfies Schrodinger equation small data smoothing effect Sobolev spaces Staffilani symbol Theorem 5.5 theory tion Tsutsumi unitary group uo G uo(x uq G well-posedness result wellposed wellposedness