5 papers
On the spectral analysis of dynamical Möbius-Sarnak process and topological entropy of Möbius fonction
el Houcein el Abdalaoui
By extending the Rokhlin-Sinai machinery relating to the entropy and countable Lebesgue component in the spectrum, we establish that the dynamical Möbius-Sarnak process has a coun…
Operator ergodic theorems with Möbius "weights"
El Houcein El Abdalaoui, Michael Lin
Motivated by Sarnak's conjecture in topological dynamics for the Möbius function , we study, for a power-bounded on a Banach space , the weak convergence $$ (*) \qquad…
A generalization of Littlewood's flat theorem,
el Houcein el Abdalaoui
We establish a generalization of Littlewood's criterion on -flatness by proving that there is no -flat polynomials, , within the class of analytic polynomials on…
On -flatness of ErdÅs-Littlewood's polynomials
el Houcein el Abdalaoui
It is shown that Erdös--Littlewood's polynomials are not -flat when is an even integer (and hence for any ). This provides a partial solution to an old pro…
On the homogeneous ergodic bilinear averages with -bounded multiplicative weights
el Houcein el Abdalaoui
We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic -bounded multiplicative function $\bo…