On the Rajchman property for self-similar measures

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 Erdös [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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Contributor : Julien Brémont <>
Submitted on : Tuesday, October 8, 2019 - 4:50:50 PM
Last modification on : Wednesday, October 9, 2019 - 1:15:46 AM

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  • HAL Id : hal-02306859, version 1
  • ARXIV : 1910.03463

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Julien Brémont. On the Rajchman property for self-similar measures. 2019. ⟨hal-02306859⟩

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