Asymptotic Schur orthogonality for lattices

Let $π:G\to \mathcal{U}(L^{2}(G/P,ν))$ be the boundary representation of a non-compact connected semisimple Lie group $G$ with finite center on its Furstenberg-Poisson boundary $(G/P,ν)$. Let $Γ\subset G$ be a lattice in $G$ (uniform or not). We show that for any \emph{continuous} functions $φ,ψ,φ',