  Let $G={\rm Spec} A$ be a linearly reductive group and let $w_G\in A^*$ be
the invariant integral on $G$. We establish the harmonic analysis on $G$ and we
compute $w_G$ when $G=Sl_n, Gl_n, O_n, Sp_{2n}$ by geometric arguments and by
means of the Fourier transform.
