  Let G be a reductive connected p-adic group. With help of the Fourier
inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke
d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415,
2001] we give a spectral decomposition on G. In particular we deduce from it
essentially that a cuspidal representation of a Levi subgroup M is in the
cuspidal support of a square integrable representation of G, if and only if it
is a pole of Harish-Chandra's \mu-function of order equal to the parabolic rank
of M. This result has been conjectured by A. Silberger in 1978. In more
explicit terms, we show that this condition is necessary and that its
sufficiency is equivalent to a combinatorical property of Harish-Chandra's
\mu-function which appears to be a consequence of a result of E. Opdam. We get
also identities between some linear combinations of matrix coeffieicients.
These identities contain informations on the formel degree of square integrable
representations and on their position in the induced representation.
