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22 September 2020
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Functions whose Fourier transform vanishes on a surface
Dmitriy M. Stolyarov ;
Date 18 Jan 2016
AbstractWe 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.
Source arXiv, 1601.4604
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