@article{51204,
  abstract     = {{Given a real semisimple connected Lie group $G$ and a discrete torsion-free
subgroup $\Gamma < G$ we prove a precise connection between growth rates of the
group $\Gamma$, polyhedral bounds on the joint spectrum of the ring of
invariant differential operators, and the decay of matrix coefficients. In
particular, this allows us to completely characterize temperedness of
$L^2(\Gamma\backslash G)$ in this general setting.}},
  author       = {{Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Duke Math. Journal }},
  title        = {{{Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}}},
  volume       = {{(to appear)}},
  year         = {{2026}},
}