arXiv subjects

E. H. Zerouali

Publications and source records attributed to E. H. Zerouali.

4 recordsLinked to original sources

arXiv2026

A Recursive approach to the matrix moment problem

In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in the classical cases of Hamburger, Stieltjes, and Hausdorff moment problems. We also discuss matricial subnormal completion and matricial $k$--hyponormal completion problems and provide an analog of Stampfli's Theorem on flat propagation for $2$--hyponormal matricial weighted shifts.

math.FA↗

arXiv2026

The Quaternionic Moment Problem

In this paper we develop an approach to the full quaternionic moment problem. We define a hierarchy $ \mathbb{H}^{k}[q^{*}, q]\subset \mathbb{H}^{k+1}[q^{*}, q]$, $k\in \mathbb{N}_{0}\cup \{\infty \}$, of two-sided $\mathbb{H}$-linear spaces of quaternionic polynomials which are invariant under conjugation of quaternions and determine the hermitian parts of these spaces explicitly. Using a generalization of Choquet's theorem on adapted spaces to quaternions we provide necessary and sufficient solvability criteria for the quaternionic moment problem of each space $ \mathbb{H}^{k}[q^{*}, q]$. The hermitian part of $ \mathbb{H}^{\infty }[q^{*}, q]$ is the real polynomial algebra $\mathbb{R}[x_{0}, x_{1}, x_{2}, x_{3}]$. This enables us to apply real algebraic geometry (Positivstellensätze) to the quaternionic moment problem on $ \mathbb{H}^{\infty }[q^{*}, q]$.

math.FA↗

arXiv2020

Jumping flatness and Aluthge transform of recursive weighted shifts

We devote this paper to Hamburger type weighted shifts. We give in particular an affirmative answer to a problem concerning subnormality of the Aluthge transform of Hamburger moment measures with finite support. we also extend the notion flatness, jumping flatness property, introduced recently by Exner et all for Hamburger-type weighted shift and provide obtain several results related to the representing measure of such weighted shifts.

math.FA↗

arXiv2018

A note on weak positive matrices, finite mass measures and hyponormal weighted shifts

We study the class of Hankel matrices for which the $k\times k$-block-matrices are positive semi-definite. We prove that a $k\times k$-block-matrix has non zero determinant if and only if all $k\times k$-block matrices have non zero determinant. We use this result to extend the notion of propagation phenomena to $k$-hyponormal weighted shifts. Finally we give a study on invariance of $k$-hyponormal weighted shifts under one rank perturbation.

math.FA↗