Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal properties of the first eigenvalue of Schr\"odinger-type
  operators   Given a separable, locally compact Hausdorff space $X$ and a positive Radon
measure $m(dx)$ on it, we study the problem of finding the potential $V(x) \ge
0$ that maximizes the first eigenvalue of the Schr\"odinger-type operator
$L+V(x)$; $L$ is the generator of a local Dirichlet form $(a, D[a])$ on $L^2(X,
m(dx))$.

14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th