A Central Limit Theorem for Some Special Complex-Valued Probability Densities1

We describe the behavior of the n-fold convolutions f n.s f) f) f) ??? ) f ^ ` _ n times under a suitable scaling as nª`, where f is an integrable complex-valued function on R. We consider only the unstable case and only two typical examples in that case. In the first example f is defined by fˆ t.sexp i