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Functions whose Fourier transform vanishes on a surface | | Dmitriy M. Stolyarov
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18 Jan 2016 | | 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. | | Source: | arXiv, 1601.4604 | | Services: | Forum | Review | PDF | Favorites | |
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