Abstract
Let G and Γ denote locally compact abelian groups, each the dual of the other. Let U ⊆ ℂ and let F be a complex-valued function defined on U. Suppose that \(\hat{\mu}\) is a Fourier-Stieltjes transform on Γ with \(\hat{\mu }\)(Γ) ⊆ U. If F ∘ \(\hat{\mu }\) is also a Fourier-Stieltjes transform, we say F operates on μ, and we let F º μ denote the measure whose transform is F ∘ \(\hat{\mu }\). This chapter discusses necessary and sufficient conditions under which F operates on all μ that belong to varying classes of measures. These results have their origin in the theorem of Wiener and Lévy.
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© 1979 Springer-Verlag New York Inc.
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Graham, C.C., McGehee, O.C. (1979). The Wiener-Lévy Theorem and Some of Its Converses. In: Essays in Commutative Harmonic Analysis. Grundlehren der mathematischen Wissenschaften, vol 238. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9976-9_9
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DOI: https://doi.org/10.1007/978-1-4612-9976-9_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9978-3
Online ISBN: 978-1-4612-9976-9
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