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On the Zero Sets of the Fourier Transform of Singular Measures

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We show that the class of sets E with the property that there exists a measure singular with respect to the Lebesgue measure whose Fourier transform tends to 0 at… Click to show full abstract

We show that the class of sets E with the property that there exists a measure singular with respect to the Lebesgue measure whose Fourier transform tends to 0 at infinity and vanishes on E contains the Helson sets.

Keywords: sets fourier; zero sets; fourier transform; singular measures; transform singular

Journal Title: Analysis Mathematica
Year Published: 2018

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