  The spatio-temporal dynamics of the deformation of a vibrated plate is
measured by a high speed Fourier transform profilometry technique. The
space-time Fourier spectrum is analyzed. It displays a behavior consistent with
the premises of the Weak Turbulence theory. A isotropic continuous spectrum of
waves is excited with a non linear dispersion relation slightly shifted from
the linear dispersion relation. The spectral width of the dispersion relation
is also measured. The non linearity of this system is weak as expected from the
theory. Finite size effects are discussed. Despite a qualitative agreement with
the theory, a quantitative mismatch is observed which origin may be due to the
dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov
casade.
