On the Fourier transform of $e^{-(x)}$

Hyeonbae Kang

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Let $μ$ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on $R$ . Then for every $ϵ > 0$ , ${x \in R | Re (μ (x)) > ϵ}$ has a vanishing interior Lebesgue measure. If $ϵ = 0$ the statement is not generally true. The result is applied to prove a theorem of Rosenthal.

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Displaying similar documents to “On the Fourier transform of e - ( x ) ”

Displaying similar documents to “On the Fourier transform of $e^{- (x)}$ ”