Sharp rate of average decay of the Fourier transform of a bounded set

2003/03/15 by Luca Brandolini, L. Brandolini, Brandolini, L. +6
Computer Science · Mathematics · #42B #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems #math.CA #msc:42B

paper · pdf · doi:10.48550/arxiv.math/0303188

10 pages. GAFA (to appear)

arxiv created 2003/03/15 · openalex publication_date 2003/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^3/2 boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.

Citations

• Lattice Points and Generalized Diophantine Conditions

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