On the spectral type of some class of rank one flows

El Houcein El Abdalaoui (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

It is shown that a certain class of Riesz product type measure on $\R$ is singular. This proves the singularity of the spectral types of some class of rank one flows. Our method is based on the extension of the Central Limit Theorem approach to the real line which gives a new extension of Salem-Zygmund Central Limit Theorem.

Mots clés: Rank one flows; spectral type; simple Lebesgue spectrum; singular spectrum; Salem-Zygmund Central Limit Theorem; Riesz products; Riesz products.

Domaines: Systèmes dynamiques [math.DS]

El Houcein El Abdalaoui. On the spectral type of some class of rank one flows. 2012. ⟨hal-00701070v1⟩