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

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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.
10 pages. GAFA (to appear)

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Classical Analysis and ODEs, 42B

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http://salesiana.dossiersoluciones.com/handle/123456789/66797

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303188
 http://arxiv.org/abs/math/0303188

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arXiv