Self-similar measures and the Rajchman property

Published 8 Oct 2019 in math.DS and math.PR | (1910.03463v8)

Abstract: For classical Bernoulli convolutions, the Rajchman property, i.e. the convergence to zero at infinity of the Fourier transform, was characterized by successive works of Erd{\"o}s [2] and Salem [12]. We prove weak forms of their results for general self-similar measures associated to affine contractions of the real line.

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Julien Brémont

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