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arXiv · 1910.03463

Self-similar measures and the Rajchman property

Julien Brémont
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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. 2019-10-08. Self-similar measures and the Rajchman property. https://arxiv.org/abs/1910.03463

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