Abstract
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.
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This work was accomplished with the support of Fondation Sciences Mathématiques de Paris.
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Roginskaya, M. Some Supports of Fourier Transforms of Singular Measures are not Rajchman. Mediterr. J. Math. 9, 403–407 (2012). https://doi.org/10.1007/s00009-011-0127-7
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DOI: https://doi.org/10.1007/s00009-011-0127-7