Decomposition of analytic measures on groups and measure spaces
Nakhlé Asmar, Stephen Montgomery-Smith (2001)
Studia Mathematica
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We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, 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 Γ. 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 derive new properties of analytic measures as well as extensions...