Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms.
Abu Muhanna, Y., Abu Muhanna, Yusuf (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Abu Muhanna, Y., Abu Muhanna, Yusuf (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
Thiruvaiyaru V. Panchapagesan (1992)
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