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arXiv · 1601.04604

Functions whose Fourier transform vanishes on a surface

Dmitriy M. Stolyarov
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Abstract

We study the subspaces of $L_p(\mathbb{R}^d)$ that consist of functions whose Fourier transforms vanish on a smooth surface of codimension $1$. We show that a subspace defined in such a manner coincides with the whole $L_p$ space for $p > \frac{2d}{d+1}$. We also prove density of smooth functions in such spaces when $p < \frac{2d}{d+1}$ for specific cases of surfaces and give an equivalent definition in terms of differential operators.

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Dmitriy M. Stolyarov. 2016-01-18. Functions whose Fourier transform vanishes on a surface. https://arxiv.org/abs/1601.04604

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