Titre : Charactérisation unifiée de certains opérateurs en relation avec l’algèbre des oscillateurs déformée via la d-orthogonalité 

Auteurs : Ali Zaghouani
, Khadija Laribi,  

Revue : Avancées en Mathématiques Pures et Appliquées 

Numéro : Numéro 3 (Juin 2026) 

Volume : 17 

Date : 2026/07/1er 

DOI : 10.21494/ISTE.OP.2026.1469 

ISSN : 1869-6090 

Résumé : In the present work, we are interested in the linear operators of the form $$$S= T(a_+)R(a_-)$$$, where $$$a_-$$$ and $$$a_+$$$ are the annihilation and creation operators, respectively defined in irreducible representation of a deformed oscillator algebra and $$$T$$$, $$$R$$$ are analytic functions. We characterize all real sequences $$$(x_k)_{k\geq0}$$$ and functions $$$T$$$ for which the matrix elements associated to the operator $$$S$$$ are expressed in terms of polynomial sets on the discrete variable $$$x_k$$$ and we show when the considered polynomial sets are $$$d$$$-orthogonal. The analytic function $$$R$$$, in most specific cases is expressed in terms of exponential or $$$q$$$-exponential functions. As a consequence, several known results are recovered and extended, including those related to the Heisenberg-Weyl algebra, and $$$q$$$-deformed oscillator algebras. Explicit realizations are given in terms ofMeixner and Charlier-type $$$d$$$-orthogonal polynomials, together with their $$$q$$$-analogues. 

Éditeur : ISTE OpenScience