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

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

2003-03-15

arxiv.org/abs/math/0303188v1

Mathematics

Classical Analysis and ODEs

10 pages. GAFA (to appear)

Scientific paper

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.

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