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- W1963736132 abstract "An L-subalgebra OL of the algebra M T of Borel measures on the circle group T is a closed subalgebra OL ⊆ M ( T ) such that μ ∈ OL implies L 1 (μ)⊆ OL . A subalgebra OL is symmetric if μ∈ OL implies μ ∈ OL , where μ (−E) = μ(−E) , ( E any Borel set). A function F : [−1, 1] → C operates on a set OL of Fourier-Stieltjes transforms if μ ∈ OL , μ ( Z )⊆[−1,1] imply F ∘ μ is a Fourier-Stieltjes transform. We have these results: If F : [−1, 1] → C operates on the Fourier-Stieltjes transforms of an infinite dimensional symmetric L -subalgebra OL , then F is analytic in a neighborhood of 0. If OL contains a measure concentrated on a Dirichlet set, then F is analytic in a neighborhood of [−1, 1]. If OL contains a continuous measure concentrated on a Kronecker set, then F is entire. Related results are given." @default.
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- W1963736132 date "1972-12-01" @default.
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- W1963736132 title "The functions which operate on Fourier-Stieltjes transforms of L-subalgebras of T" @default.
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- W1963736132 doi "https://doi.org/10.1016/0022-1236(72)90066-3" @default.
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