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Idele characters in spectral synthesis on 𝐑 / 2 π 𝐙

John J. Benedetto (1973)

Annales de l'institut Fourier

Let s C , x R / 2 π Z . We construct Dirichlet series F ( x , x ) where for each fixed s in a half plane, Re F ( x , x ) , as a function of x , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in F are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when Re s 1 .

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