Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weyl Law on Asymptotically Euclidean Manifolds   We study the asymptotic behaviour of the eigenvalue counting function for
self-adjoint elliptic linear operators defined through classical weighted
symbols of order $(1,1)$, on an asymptotically Euclidean manifold. We first
prove a two term Weyl formula, improving previously known remainder estimates.
Subsequently, we show that under a geometric assumption on the Hamiltonian flow
at infinity there is a refined Weyl asymptotics with three terms. The proof of
the theorem uses a careful analysis of the flow behaviour in the corner
component of the boundary of the double compactification of the cotangent
bundle. Finally, we illustrate the results by analysing the operator
$Q=(1+|x|^2)(1-\Delta)$ on $\mathbb{R}^d$.

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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga