New bounds for the discrete Fourier restriction to the sphere in four and five dimensions
Jean Bourgain, Ciprian Demeter
TL;DR
This paper advances the understanding of discrete Fourier restriction to spheres in four and five dimensions by establishing improved bounds using incidence theory and Siegel's mass formula.
Contribution
It introduces novel bounds for Fourier restriction problems in higher dimensions leveraging incidence theory and Siegel's mass formula.
Findings
Enhanced bounds for Fourier restriction in 4D and 5D
Application of incidence theory to harmonic analysis
Use of Siegel's mass formula in restriction estimates
Abstract
We improve the range for the discrete Fourier restriction to the four and five dimensional spheres. We rely on two new ingredients, incidence theory and Siegel's mass formula.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Mathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research