STOCHASTIC MATRIX TRANSFORMS
It is shown that Daboussi's theorem characterizing almost-periodic multiplicative functions f with non-void spectrum by the convergence of certain sums over values of f at prime powers may be deduced from (a variant of) the Daboussi-Elliott theorem on mean-values of multiplicative functions. The proof uses the relationship theorem of Heppner and the first author and an extension of Daboussi's theorem on the vanishing of the Fourier-coefficients ^ ( ß ) for certain multiplicative functions f, if ß is irrational. AMS Classification: lo K 35, lo H 45.