arXiv subjects

Mostafa Maslouhi

Publications and source records attributed to Mostafa Maslouhi.

5 recordsLinked to original sources

arXiv2024

A Law Limit Theorem for a sequence of random variables

An application of Levy's continuity theorem and Hankel transform allow us to establish a law limit theorem for the sequence $V_n=f(U)\sin(n U)$, where $U$ is uniformly distributed in $(0,1)$ and $f$ a given function. Further, we investigate the inverse problem by specifying a limit distribution and look for the suitable function $f$ ensuring the convergence in law to the specified distribution. Our work recovers and extends existing similar works, in particular we make it possible to sample from known laws including Gaussian and Cauchy distributions.

math.PR↗

arXiv2024

The HRT conjecture for a class of meromorphic functions

The HRT conjecture states that any finite collection of time-frequency shifts of a non-zero square-integrable function on the real line is linearly independent. In this paper, we establish the linear independence of finite systems of time-frequency shifts of a non-zero meromorphic function. Consequently, we prove that the conjecture is true for any square-integrable function on $\mathbb{R}$ that can be extended to an analytic function on $\mathbb{C}$ except on finitely many points.

math.CV↗

arXiv2023

On the Generalized Ornstein-Uhlenbeck Semigroup

We give several functional inequalities related to the Ornstein-Uhlenbeck semigroup in the Dunkl differential-difference operators setting. As an application of these inequalities, we derive out a Sobolev-logarithmic and an hypercontractivity properties for this semigroup

math.FA↗

arXiv2022

On root frames in $\mathbb{R}^d$

\emph{A root frame} for $\mathbb{R}^d$ is a finite frame whose vectors form a root system. In this note we establish some elementary properties of this class of frames and prove that root frames constitute a subclass of scalable frames. In addition, we show that root frames are examples of a larger class of frames called \emph{eigenframes}.

math.GM↗

arXiv2016

On The Dunkl Intertwining Opereator

Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and intertwines with this latter by the so-called intertwining operator. In this paper, we give an integral representation for the operator $V_k\circ e^{Δ/2}$ for an arbitrary Weyl group and a large class of regular weights $k$ containing those of non negative real parts. Our representing measures are absolute continuous with respect the Lebesgue measure in $\Rd$, which allows us to derive out new results about the intertwining operator $V_k$ and the Dunkl kernel $E_k$. We show in particular that the operator $V_k\circ e^{Δ/2}$ extends uniquely as a bounded operator to a large class of functions which are not necessarily differentiables. In the case of non negative weights, this operator is shown to be positivity-preserving.

math.FA↗