Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^p$ spectral theory and heat dynamics of locally symmetric spaces   In this paper we first derive several results concerning the $L^p$ spectrum
of arithmetic locally symmetric spaces whose $\Q$-rank equals one. In
particular, we show that there is an open subset of $\C$ consisting of
eigenvalues of the $L^p$ Laplacian if $p <2$ and that corresponding
eigenfunctions are given by certain Eisenstein series. On the other hand, if
$p>2$ there is at most a discrete set of real eigenvalues of the $L^p$
Laplacian. These results are used in the second part of this paper in order to
show that the dynamics of the $L^p$ heat semigroups for $p<2$ is very different
from the dynamics of the $L^p$ heat semigroups if $p\geq 2$.

0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th