Some Supports of Fourier Transforms of Singular Measures are not Rajchman
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The notion of Riesz sets tells us that a support of Fourier transform of a measure with non-trivial singular part has to be large. The notion of Rajchman sets tells us that if the Fourier transform tends to zero at infinity outside a small set, then it tends to zero even on the small set. Here we present a new angle of an old question: Whether every Rajchman set should be Riesz.
Mathematics Subject Classification (2010)Primary 42A16 Secondary 43A05
KeywordsRajchman sets Riesz sets Riesz products singular measures support of Fourier transform
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