Weak mixing implies weak mixing of higher orders along tempered functions

Abstract

AbstractWe extend the weakly mixing PET (polynomial ergodic theorem) obtained in Bergelson [Weakly mixing PET.Ergod. Th. & Dynam. Sys.7(1987), 337–349] to much wider families of functions. Besides throwing new light on the question of ‘how much higher-degree mixing is hidden in weak mixing’, the obtained results also show the way to possible new extensions of the polynomial Szemerédi theorem obtained in Bergelson and Leibman [Polynomial extensions of van der Waerden’s and Szemerédi’s theorems.J. Amer. Math. Soc.9(1996), 725–753].