Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Abdalaoui, El Houcein El"'
Autor:
Abdalaoui, el Houcein el, Lin, Michael
Let $T$ be the Koopman operator of a measure preserving transformation $\theta$ of a probability space $(X,\Sigma,\mu)$. We study the convergence properties of the averages $M_nf:=\frac1n\sum_{k=0}^{n-1}T^kf$ when $f \in L^r(\mu)$, $0
Externí odkaz:
http://arxiv.org/abs/2401.00567
Autor:
Abdalaoui, el Houcein el
We present a simple proof on the existence of $L^1$-flat analytic polynomials with coefficients $0,1$ on the circle and on the real line and we give an example of a conservative ergodic map and flow whose unitary operators admits a simple Lebesgue sp
Externí odkaz:
http://arxiv.org/abs/2210.15480
Autor:
Abdalaoui, el Houcein el, Adams, Terry
We establish that there are non-mixing maps that are mixing on appropriate sequences including sequences $(s_i)$ which satisfy the Rajchman dissociated property. Our examples are based on the staircase rank one construction, $M$-towers constructions
Externí odkaz:
http://arxiv.org/abs/2206.01177
Autor:
Abdalaoui, el Houcein el
It is shown that the $L^\alpha$-norms polynomials Rudin conjecture fails. Our counterexample is inspired by Bourgain's work on NLS. Precisely, his study of the Strichartz's inequality of the $L^6$-norm of the periodic solutions given by the two dimen
Externí odkaz:
http://arxiv.org/abs/2110.05486
Autor:
Abdalaoui, el Houcein el
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 only if its Mahler measure is zero. As a consequence, we exhibit a new s
Externí odkaz:
http://arxiv.org/abs/2108.13416
Autor:
Abdalaoui, el Houcein el
We extend the classical van der Corput inequality to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the $\mathbb{R}$-action which assert that for any family of maps $(T_t)_{t \in \mathbb{R}}$ acting on the
Externí odkaz:
http://arxiv.org/abs/2107.08798
We prove that any dendrite map for which the set of endpoints is closed and countable fulfilled Sarnak M\"{o}bius disjointness. This extended a result by el Abdalaoui-Askri and Marzougui \cite{ela-GH}. We further notice that the Smital-Ruelle propert
Externí odkaz:
http://arxiv.org/abs/2012.14354
Autor:
Abdalaoui, el Houcein el
We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic $1$-bounded multiplicative function $\boldsymbol{\nu}$, for any map $T$ acting on a probability space $(X,\mat
Externí odkaz:
http://arxiv.org/abs/2012.06323
Autor:
Abdalaoui, el Houcein el
It is shown that for any $\alpha \in ]\frac12,1[$ there exists a symmetric probability measure $\sigma$ on the torus such that the Hausdorff dimension of the support of $\sigma$ is $\alpha$ and $\sigma*\sigma$ is absolutely continuous with flat conti
Externí odkaz:
http://arxiv.org/abs/2012.02042
Autor:
Abdalaoui, el Houcein el
We establish a generalization of Bourgain double recurrence theorem by proving that for any map $T$ acting on a probability space $(X,\mathcal{A},\mu)$, and for any non-constant polynomials $P, Q$ mapping natural numbers to themselves, for any $f,g \
Externí odkaz:
http://arxiv.org/abs/2008.04886