Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functions whose Fourier transform vanishes on a surface   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.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: physics
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas