The F. and M. Riesz theorem revisited.

Hewitt, Edwin; Koshi, Shōzō; Yuji, Takahashi

doi:10.7146/math.scand.a-12172

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“…Indeed common generalizations of both these ideas have been provided, for example, by Yamaguchi [23], considering the action of any locally compact abelian group with ordered dual, on a locally compact topological space. For more generalizations we refer the reader to Hewitt, Koshi, and Takahashi [19].…”

Section: Introductionmentioning

confidence: 99%

Decomposition of analytic measures on groups and measure spaces

Montgomery‐Smith

2001

Studia Math.

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Abstract.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 of previous work of Helson and Lowdenslager, de Leeuw and Glicksberg, and Forelli.

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Section: Introductionmentioning

confidence: 99%