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arXiv · 1102.3577

Some supports of Fourier transforms of singular measures are not Rajchman

Maria Roginskaya
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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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Maria Roginskaya. 2011-02-17. Some supports of Fourier transforms of singular measures are not Rajchman. https://doi.org/10.1007/s00009-011-0127-7

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