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Decomposition of analytic measures on groups and measure spaces

Nakhlé Asmar and Stephen Montgomery-Smith
Department of Mathematics
University of Missouri
Columbia, MO 65211

Dedicated to the memory of Edwin Hewitt


In this paper, we consider an arbitrary locally compact abelian group $ G$, with an ordered dual group $ \Gamma$, acting on a space of measures. Under suitable conditions, we define the notion of analytic measures using the representation of $ G$ and the order on $ \Gamma$. 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.

A.M.S. Subject Classification: 43A17, 43A32,

Keywords: orders, transference, measure space, sup path attaining, F.&M. Riesz Theorem

Stephen Montgomery-Smith 2002-10-30