Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubling condition at the origin for non-negative positive definite
  functions   We study upper and lower estimates as well as the asymptotic behavior of the
sharp constant $C=C_n(U,V)$ in the doubling-type condition at the origin \[
\frac{1}{|V|}\int_{V}f(x)\,dx\le C\,\frac{1}{|U|}\int_{U}f(x)\,dx, \] where
$U,V\subset \mathbb{R}^{n}$ are $0$-symmetric convex bodies and $f$ is a
non-negative positive definite function.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol