A spectral decomposition of orbital integrals for $PGL(2,F)$

David Kazhdan, Stephen DeBacker

Let $F$ be a local non-archimedian field, $G$ a semisimple $F$-group, $dg$ a Haar measure on $G$ and $\mathcal{S}(G)$ be the space of locally constant complex valued functions $f$ o…