3 citations · 3 across the 3 of their papers we have counts for
3 papers
A new class of rank one transformations with singular spectrum
El Houcein El Abdalaoui
We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.
A new class of Ornstein transformations with singular spectrum
El Houcein El Abdalaoui, François Parreau, A. A. Prikhod'Ko
It is shown that for any family of probability measures in Ornstein type constructions the corresponding transformation has almost surely a singular spectrum. This is a new general…
Weak mixing of maps with bounded cutting parameter
El Houcein El Abdalaoui, Arnaldo A. N. Noguiera, Thierry T. D. De Larue
In the class of Ornstein transformations the mixing property satisfies a 0-1 law. Here we consider Ornstein's construction with bounded cutting parameter. In fact, these latter tra…