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On Fourier-Stieltjes Transforms
Published online by Cambridge University Press: 20 November 2018
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Let be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions ϕ(− ∞) = 0 , ϕ(t + 0) = ϕ(t).
Let be the class of Fourier-Stieltjes transforms of elements of i.e. the elements of and are connected by the relation
where ϕ ∊ and Φ ∊ .It is well known, and easy to verify that this mapping from to is one to one (1, p. 67, Satz 18).
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- Copyright © Canadian Mathematical Society 1955
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