Decomposition of Analytic Measures on Groups and Measure Spaces

Abstract

In this paper, we consider an arbitrary locally compact abelian group G, with an ordered dual group , acting on a space of measures. Under suitable conditions, we dene the notion of analytic measures using the representation of G and the order on . Our goal is to study analytic measures by applying a new transference principle for subspaces of measures, along with results from probability and Littlewood-Paley theory. As a consequence, we will derive new properties of analytic measures as well as extensions of previous work of Helson and Lowdenslager, de Leeuw and Glicksberg, and Forelli