Some supports of Fourier transforms of singular measures are not Rajchman

Details Some supports of Fourier transforms of singular measures are not Rajchman Some supports of Fourier transforms of singular measures are not Rajchman

2011-02-17

arxiv.org/abs/1102.3577v1

Mathematics

Functional Analysis

Scientific paper

10.1007/s00009-011-0127-7

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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