Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nearly radial product functions   If $f\in L^2(R^d)$ and if the function $f(x)f(y)$ is close in $L^2(R^{2d})$
norm to a radially symmetric function of $(x,y)$ then $f$ is close in $L^2$
norm to a centered Gaussian function. This is proved in a quantitative form
with the optimal exponent measuring closeness.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con