Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherical functions and rapid decay for hyperbolic groups   We investigate properties of some spherical fonctions defined on hyperbolic
groups using boundary representations on the Gromov boundary endowed with the
Patterson-Sullivan measure class. We prove sharp decay estimates for spherical
functions as well as spectral inequalities associated with boundary
representations. This point of view on the boundary allows us to view the
so-called \emph{property RD} (also called \emph{Haagerup's inequality}) as a
particular case of a more general behavior of spherical functions on hyperbolic
groups. In particular, we give a constructive proof using a boundary unitary
representation of a result due to de la Harpe and Jolissaint asserting that
hyperbolic groups satisfy \emph{property RD}. Finally, we prove that the family
of boundary representations studied in this paper, which can be regarded as a
one parameter deformation of the boundary unitary representation, are slow
growth representations acting on a Hilbert space admitting a proper
$1$-cocycle.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg