60 citations · 97 across the 30 of their papers we have counts for
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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…
Some Notes on Flat Polynomials
e. H. el Abdalaoui, M. G. Nadkarni
Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big…
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.