Improved estimates for the discrete Fourier restriction to the higher dimensional sphere

zbMath1319.42006arXiv1205.2414MaRDI QIDQ2509821

Ciprian Demeter, Jean Bourgain

Publication date: 30 July 2014

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.2414

zbMATH Keywords

exponential sumsKloosterman sums\(n\)-dimensional spherediscrete Fourier restriction

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Gauss and Kloosterman sums; generalizations (11L05) Fourier series and coefficients in several variables (42B05)

Related Items (9)

The nonlinear Schrödinger equation on tori: Integrating harmonic analysis, geometry, and probability ⋮ Uniform \(L^p\) resolvent estimates on the torus ⋮ Bounds for spectral projectors on tori ⋮ Bounds for spectral projectors on generic tori ⋮ Discrete restriction estimates for forms in many variables ⋮ On Fourier restriction type problems on compact Lie groups ⋮ Conjecture and improved extension theorems for paraboloids in the finite field setting ⋮ The orthonormal Strichartz inequality on torus ⋮ The proof of the \(l^2\) decoupling conjecture

Cites Work

• Unnamed Item
• On the multilinear restriction and Kakeya conjectures
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums

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