TY  - Type of reference 
TI  - [FORTHCOMING] A unified characterization of certain operators related to deformed oscillator algebras via d-orthogonality 
AU  - Ali Zaghouani
 
AU  - Khadija Laribi 
AB  - 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. 
DO  - TBA 
JF  - Advances in Pure and Applied Mathematics 
KW  - Deformed oscillator algebras, matrix elements of operators, coherent states, d-orthogonal polynomial sets, generating functions, Deformed oscillator algebras, matrix elements of operators, coherent states, d-orthogonal polynomial sets, generating functions,  
L1  -  
LA  - en 
PB  - ISTE OpenScience 
DA  - 2026/04/7 
SN  - 1869-6090 
TT  - [FORTHCOMING] Charactérisation unifiée de certains opérateurs en relation avec l’algèbre des oscillateurs déformée via la d-orthogonalité 
UR  - https://www.openscience.fr/A-unified-characterization-of-certain-operators-related-to-deformed-oscillator 
IS  - Forthcoming papers<br> 
VL  -  
ER  -