On the structure of polynomial multicorrelation sequences arising from nilpotent actions

Abstract

We prove that every polynomial multicorrelation sequence arising from nilpotent actions admits a decomposition into a generalized nilsequence and a null-sequence. This resolves a long-standing question of Frantzikinakis concerning the structure of polynomial multicorrelation sequences of commuting transformations. Our proof builds upon ideas underlying the norm convergence theorem of Walsh.