English

Self-similar measures and the Rajchman property

Dynamical Systems 2020-12-14 v8 Probability

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.

Keywords

Cite

@article{arxiv.1910.03463,
  title  = {Self-similar measures and the Rajchman property},
  author = {Julien Brémont},
  journal= {arXiv preprint arXiv:1910.03463},
  year   = {2020}
}