  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 $f$ on $G$ with compact support. For any regular
elliptic congugacy class $\Omega =h^G\subset G$ we denote by $I_\Omega$ the
$G$-invariant functional on $\mathcal S (G)$ given by $$I_\Omega (f)=\int_G
f(g^{-1}hg)dg$$ This paper provides the spectral decomposition of functionals
$I_\Omega$ in the case $G=PGL(2,F)$ and in the last section first steps of such
an analysis for the general case.
