3 citations · 5 across the 8 of their papers we have counts for
14 papers
Asymptotic Schur orthogonality for lattices
A. BENDIKOV, A. BOYER, CH. PITTET
Let be the boundary representation of a non-compact connected semisimple Lie group with finite center on its Furstenberg-Poisson boundary $(G…
Riesz operators and -boundary representations for hyperbolic groups
Adrien Boyer, Jean-Martin Paoli
We investigate Lp-boundary representations of hyperbolic groups. We prove that such representations are irreducible if and only if the corresponding Riesz operators are injective.
Riesz operators and some spherical representations for hyperbolic groups
Adrien Boyer, Jean-Claude Picaud
We introduce the Riesz operator in the context of Gromov hyperbolic groups in order to investigate a one parameter family of non unitary boundary Hilbertian representations of hype…
Radial rapid decay does not imply rapid decay
Adrien Boyer, Antoine Pinochet Lobos, Christophe Pittet
We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group , where $A := \mathbb{F}_q[X,X^…
Spherical functions and rapid decay for hyperbolic groups
Adrien Boyer
We investigate properties of some spherical fonctions defined on hyperbolic groups using boundary representations on the Gromov boundary endowed with the Patterson-Sullivan measure…
Asymptotic Schur orthogonality in hyperbolic groups with application to monotony
Adrien Boyer, Łukasz Garncarek
We prove a generalization of Schur orthogonality relations for certain classes of representations of Gromov hyperbolic groups. We apply the obtained results to show that representa…
Ergodic boundary representations
Adrien Boyer, Gabriele Link, Christophe Pittet
We prove a von Neumann type ergodic theorem for averages of unitary operators arising from the Furstenberg-Poisson boundary representation (the quasi-regular representation) of any…
Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups
Adrien Boyer
We prove that the Harish-Chandra--Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced -algebra of the discrete su…
Equidistribution, ergodicity and irreducibility associated with Gibbs measures
Adrien Boyer, Dustin Mayeda
We generalize an equidistribution theorem à la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in th…
An ergodic theorem for the quasi-regular representation of the free group
Adrien Boyer, Antoine Pinochet Lobos
In \cite{BAMU}, an ergodic theorem à la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover…
On the square root of Poisson kernel in -hyperbolic spaces and some aspects of boundary representations
Adrien Boyer
In this note, we prove a theorem à la Fatou for the square root of Poisson Kernel in the context of quasi-convex cocompact discrete groups of isometries of -hyperbolic spaces. A…
Semisimple Lie groups satisfy property RD, a short proof
Adrien Boyer
We give a short elementary proof of the fact that connected semisimple real Lie groups satisfy property RD. The proof is based on a process of linearization.
Equidistribution, ergodicity and irreducibility in CAT(-1) spaces
Adrien Boyer
We prove an equidistribution theorem a la Bader-Muchnik for operator-valued measures associated with boundary representations in the context of discrete groups of isometries of CAT…
Quasi-regular representations and property RD
Adrien Boyer
We study \emph{property RD} in terms of rapid decay of matrix coefficients. We give new formulations of property RD in terms of a -integra\-bility condition of a Banach repr…