Structure and Spectrum of Nonergodic Nilsystems

Abstract

We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component and a Lebesgue component of infinite multiplicity. Our main result extends this decomposition to nonergodic nilsystems.

We decided to remove Corollary C as there is an overlooked case that does not seem to follow from our main results