@ARTICLE{TBA, 

TITLE={[FORTHCOMING] A unified characterization of certain operators related to deformed oscillator algebras via d-orthogonality}, 
  
AUTHOR={Ali Zaghouani
, Khadija Laribi, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={}, 

NUMBER={Forthcoming papers<br>}, 
	
YEAR={2026}, 

URL={https://www.openscience.fr/A-unified-characterization-of-certain-operators-related-to-deformed-oscillator}, 
	
DOI={TBA}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={In the presentwork,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.}}