A LOCAL LIMIT-THEOREM ON THE SEMIDIRECT P RODUCT OF R(ASTERISK+) AND R(D)

Let G be the demi-direct product of R(+) and R(d) and mu a probabilit y measure on G which is absolutely continuous with respect to the righ t Haar measure. Let mu(n) be the n-th power of convolution of mu. Und er moment assumptions on mu, one can prove that there exists rho E[0, 1] such that the sequence of Radon measures ((n(3/2)/rho(n))mu(n))n g reater than or equal to 1 converges weakly to a non trivial measure wh en n goes to +infinity.