Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Fourier transform of function of two variables which depend only
  on the maximum of these variables   For functions $f(x_{1},x_{2})=f_{0}\big(\max\{|x_{1}|,|x_{2}|\}\big)$ from
$L_{1}(\mathbb{R}^{2})$, sufficient and necessary conditions for the belonging
of their Fourier transform $\widehat{f}$ to $L_{1}(\mathbb{R}^{2})$ as well as
of a function $t\cdot \sup\limits_{y_{1}^{2}+y_{2}^{2}\geq
t^{2}}\big|\widehat{f}(y_{1},y_{2})\big|$ to $L_{1}(\mathbb{R}^{1}_{+})$. As
for the positivity of $\widehat{f}$ on $\mathbb{R}^{2}$, it is completely
reduced to the same question on $\mathbb{R}^{1}$ for a function
$f_{1}(x)=|x|f_{0}\big(|x|\big)+\int\limits_{|x|}^{\infty}f_{0}(t)dt$.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics