Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Sobolev norms for Lie group representations   We define Sobolev norms of arbitrary real order for a Banach representation
$(\pi, E)$ of a Lie group, with regard to a single differential operator
$D=d\pi(R^2+\Delta)$. Here, $\Delta$ is a Laplace element in the universal
enveloping algebra, and $R>0$ depends explicitly on the growth rate of the
representation. In particular, we obtain a spectral gap for $D$ on the space of
smooth vectors of $E$. The main tool is a novel factorization of the delta
distribution on a Lie group.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con