Functions whose Fourier transform vanishes on a surface
Classical Analysis and ODEs
2016-01-26 v2
Abstract
We study the subspaces of that consist of functions whose Fourier transforms vanish on a smooth surface of codimension . We show that a subspace defined in such a manner coincides with the whole space for . We also prove density of smooth functions in such spaces when for specific cases of surfaces and give an equivalent definition in terms of differential operators.
Cite
@article{arxiv.1601.04604,
title = {Functions whose Fourier transform vanishes on a surface},
author = {Dmitriy M. Stolyarov},
journal= {arXiv preprint arXiv:1601.04604},
year = {2016}
}
Comments
11 pages. Theorems 3 and 4 of this preprint follow by duality from more general Theorem 1 in "$L^p$-integrability, supports of Fourier transforms and uniqueness for convolution equations" by M. L. Agranovsky and E. K. Narayanan in Journ. Four. Anal. Appl. vol.10:3 (2004), 315--324