There is a natural interplay between the L∞ eigenvalue group of a non‐singular transformation and its L2 spectra via systems of imprimitivity. This aids us, on the one hand, to compute some new eigenvalue groups together with their natural Polish topologies, and, on the other, to prove a result on the extension of cocycles. Prime group rotations preserving infinite measures are constructed. Other eigenvalue groups are also considered, and information is gleaned about their underlying transformations from the nature of their duals.
In this paper it is shown that the maximal spectral type of a general rank one transformation is given by a kind of generalized Riesz product, with possibly some discrete measure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.