Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the expansion of solutions of Laplace-like equations into traces of
  separable higher dimensional functions   This paper deals with the equation $-\Delta u+\mu u=f$ on high-dimensional
spaces $\mathbb{R}^m$ where $\mu$ is a positive constant. If the right-hand
side $f$ is a rapidly converging series of separable functions, the solution
$u$ can be represented in the same way. These constructions are based on
approximations of the function $1/r$ by sums of exponential functions. The aim
of this paper is to prove results of similar kind for more general right-hand
sides $f(x)=F(Tx)$ that are composed of a separable function on a space of a
dimension $n$ greater than $m$ and a linear mapping given by a matrix $T$ of
full rank. These results are based on the observation that in the
high-dimensional case, for $\omega$ in most of the $\mathbb{R}^n$, the
euclidian norm of the vector $T^t\omega$ in the lower dimensional space
$\mathbb{R}^m$ behaves like the euclidian norm of $\omega$.

5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat