Solution to a functional equation and its application to stable and stable-type distributions

The main result of the paper completely characterizes all continuous complex-valued functions [phi](t) with domain or satisfying[phi](t)=([phi](a1t))[gamma]1=([phi](a2t))[gamma]2,where a1[not equal to]1, a2[not equal to]1, [gamma]1,[gamma]2 are positive numbers with irrational log a1/log a2.Characterization Stable distributions Sub-independence