Self-similar measures and the Rajchman property

Julien Brémont (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: AMS 2010 subject classifications : 11K16; 37A45; 42A38; 42A61; 60K20 Rajchman measure; self-similar measure; Pisot number; Plastic number

Domaines: Systèmes dynamiques [math.DS]; Probabilités [math.PR]

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