Decomposition of analytic measures on groups and measure spaces

Volume 146 / 2001

Nakhlé Asmar, Stephen Montgomery-Smith 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.

Authors

  • Nakhlé AsmarDepartment of Mathematics
    University of Missouri
    Columbia, MO 65211, U.S.A.
    e-mail
  • Stephen Montgomery-SmithDepartment of Mathematics
    University of Missouri
    Columbia, MO 65211, U.S.A.
    e-mail

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