Decomposition of analytic measures on groups and measure spaces
Volume 146 / 2001
Studia Mathematica 146 (2001), 261-284
MSC: 43A17, 43A32.
DOI: 10.4064/sm146-3-4
Abstract
We consider an arbitrary locally compact abelian group $G$, with an ordered dual group ${\mit \Gamma }$, 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 ${\mit \Gamma }$. 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 derive new properties of analytic measures as well as extensions of previous work of Helson and Lowdenslager, de Leeuw and Glicksberg, and Forelli.
