On the non-reducibility of non-stationary correlation functions to stationary ones under a class of mean-operator transformations

Some special functional equations involving means and related to a problem of reducibility of some classes of correlation functions are considered. We show some characterizations of the reducibility problem under several choices of the mean operators and different weak regularity assumptions imposed on the involving functions. We find that mean-generated correlation functions are completely irreducible, in the sense that, for this broad class of correlation functions, there does not exist a non-trivial solution associated to the Perrin-Senoussi problem. © 2009 Springer-Verlag.