Hahn's problem with respect to some perturbations of the raising operator $(X-c)$

Baghdadi Aloui   ; Jihad Souissi

Ural mathematical journal, Tome 6 (2020) no. 2, pp. 15-24

Résumé

In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator $X-c$, where $c$ is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the $q$-Hermite (resp. Charlier) polynomial is the only $H_{\alpha,q}$-classical (resp. \linebreak $\mathcal{S}_{\lambda}$-classical) orthogonal polynomial, where $H_{\alpha, q}:=X+\alpha H_q$ and $\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}$.

Détail

Keywords: linear functional, $\mathcal{O}$-classical polynomials, Raising operators, $q$-Hermite polynomials, Charlier polynomials.
Mots-clés : orthogonal polynomials

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