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Journal Articles Annales Henri Lebesgue Year : 2021

Self-similar measures and the Rajchman property

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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Dates and versions

hal-02306859 , version 1 (08-10-2019)
hal-02306859 , version 2 (30-10-2019)
hal-02306859 , version 3 (16-12-2019)
hal-02306859 , version 4 (16-01-2020)
hal-02306859 , version 5 (31-01-2020)
hal-02306859 , version 6 (20-02-2020)
hal-02306859 , version 7 (06-04-2020)
hal-02306859 , version 8 (07-12-2020)

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Cite

Julien Brémont. Self-similar measures and the Rajchman property. Annales Henri Lebesgue, 2021, 4, pp.973-1004. ⟨hal-02306859v8⟩
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