Fourier transform, $L^2$ restriction theorem, and scaling
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We show, using a Knapp-type homogeneity argument, that the restriction theorem implies a growth condition on the hypersurface in question. We further use this result to show that the optimal restriction theorem implies the sharp isotropic decay rate for the Fourier transform of the Lebesgue measure carried by compact convex finite hypersurfaces.
Cite
@article{arxiv.math/0104097,
title = {Fourier transform, $L^2$ restriction theorem, and scaling},
author = {Alex Iosevich},
journal= {arXiv preprint arXiv:math/0104097},
year = {2007}
}