Discrete Fourier restriction associated with Schrodinger equations

Details Discrete Fourier restriction associated with Schrodinger equations Discrete Fourier restriction associated with Schrodinger equations

2011-08-17

arxiv.org/abs/1108.5164v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result on Strichartz estimates associated with Schr\"odinger equations on torus. Some sharp estimates on $L^{\frac{2(d+2)}{d}}$ norm of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on $L^2(\mathbb Z)$.

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