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Ural Math. J., 2020, Volume 6, Issue 2, Pages 15–24 (Mi umj122)  

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

Baghdadi Aloui, Jihad Souissi

Université de Gabès

Abstract: 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 $\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}$.

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

DOI: https://doi.org/10.15826/umj.2020.2.002

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Citation: Baghdadi Aloui, Jihad Souissi, “Hahn's problem with respect to some perturbations of the raising operator $(X-c)$”, Ural Math. J., 6:2 (2020), 15–24

Citation in format AMSBIB
\Bibitem{AloSou20}
\by Baghdadi~Aloui, Jihad~Souissi
\paper Hahn's problem with respect to some perturbations of the raising operator $(X-c)$
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 2
\pages 15--24
\mathnet{http://mi.mathnet.ru/umj122}
\crossref{https://doi.org/10.15826/umj.2020.2.002}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR4194010}
\elib{https://elibrary.ru/item.asp?id=44611146}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099543118}


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