60 citations · 97 across the 30 of their papers we have counts for
28 papers · 1 filter
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 count…
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 \q…
Mean ergodic theorems in and ,
el Houcein el Abdalaoui, Michael Lin
Let be the Koopman operator of a measure preserving transformation of a probability space . We study the convergence properties of the averages $M_nf:=\frac1n\sum_…
-flat polynomials and simple Lebesgue spectrum for conservative maps exist: A simple proof
el Houcein el Abdalaoui
We present a simple proof on the existence of -flat analytic polynomials with coefficients on the circle and on the real line and we give an example of a conservative er…
Mixing sequences for non-mixing transformations and group actions
el Houcein el Abdalaoui, Terry Adams
We establish that there are non-mixing maps that are mixing on appropriate sequences including sequences which satisfy the Rajchman dissociated property. Our examples are b…
On the Mahler measure of the spectrum of rank one maps
el Houcein el Abdalaoui
We extend partially the Kakutani-Zygmund dichotomy theorem to a class of generalized Riesz-product type measures by proving that the generalized Riesz-product is singular if and on…
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…
Sarnak's Möbius disjointness for dynamical systems with singular spectrum and dissection of Möbius flow
el Houcein el Abdalaoui, Mahesh Nerurkar
It is shown that Sarnak's Möbius orthogonality conjecture is fulfilled for the compact metric dynamical systems for which every invariant measure has singular spectra. This is acco…
Weakly tame systems, their characterizations and application
e. H. el Abdalaoui, M. Nerurkar
We explore the notion of discrete spectrum and its various characterizations for ergodic measure-preserving actions of an amenable group on a compact metric space. We introduce a n…
On Veech's proof of Sarnak's theorem on the Möbius flow
el Houcein el Abdalaoui
We present Veech's proof of Sarnak's theorem on the Möbius flow which say that there is a unique admissible measure on the Möbius flow. As a consequence, we obtain that Sarnak's co…
Oscillating sequences, Gowers norms and Sarnak's conjecture
el Houcein el Abdalaoui
It is shown that there is an oscillating sequence of higher order which is not orthogonal to the class of dynamical flow with topological entropy zero. We further establish that an…
Möbius disjointness for models of an ergodic system and beyond
El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
Given a topological dynamical system and an arithmetic function , we study the strong MOMO property (relatively to $\boldsymbol…
A cubic nonconventional ergodic average with multiplicative or Mangoldt weights
el Houcein el Abdalaoui, XiangDong Ye
We show that the cubic nonconventional ergodic averages of any order with a bounded multiplicative function weight converge almost surely to zero provided that the multiplicative f…
A simple proof of Bourgain's theorem on the singularity of the spectrum of Ornstein's maps
El Houcein El Abdalaoui
We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.
On flat polynomials with non-Negative coefficients
e. H. el Abdalaoui, M. G. Nadkarni
We formulate and prove a necessary condition for a sequence of analytic trigonometric polynomials with real non-negative coefficients to be flat a.e.
Spectral ergodic Banach problem and flat polynomials
el Houcein el Abdalaoui
We exhibit a sequence of flat polynomials with coefficients . We thus get that there exist a sequences of Newman polynomials that are -flat, . This settles an…
The Chowla and the Sarnak conjectures from ergodic theory point of view
El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk +1
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizati…
On the pointwise convergence of multiple ergodic averages
E. H. El Abdalaoui
It is shown that there exist a subsequence for which the multiple ergodic averages of commuting invertible measure preserving transformations of a Lebesgue probability space conver…
A non-singular transformation whose spectrum has Lebesgue component of multiplicity one
E. H. El Abdalaoui, M. G. Nadkarni
In this note we give an example of an ergodic non-singular map whose unitary operator admits a Lebesgue component of multiplicity one in its spectrum.
A dynamical point of view on the set of B-free integers
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We extend the study of the square-free flow, recently introduced by Sarnak, to the more general context of B-free integers, that is to say integers with no factor in a given family…
Calculus of Generalized Riesz Products
e. H. el Abdalaoui, M. G. Nadkarni
In this paper we discuss generalized Riesz products bringing into consideration theory, the notion of Mahler measure, and the zeros of polynomials appearing in the generalize…
Spectral properties of the Möbius function and a random Möbius model
E. H. el Abdalaoui, M. Disertori
Assuming Sarnak conjecture is true for any singular dynamical process, we prove that the spectral measure of the Möbius function is equivalent to Lebesgue measure. Conversely, unde…
0-1 sequences of the Thue-Morse type and Sarnak's conjecture
El Houcein El Abdalaoui, Stanisław Kasjan, Mariusz Lemańczyk
We show that the images via of the continuous part of the spectral measures of the dynamical systems generated by the 0-1 sequences of the Thue-Morse type are pairwi…
On spectral disjointness of powers for rank-one transformations and Möbius orthogonality
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking param…