A characterization of Meixner orthogonal polynomials via a certain transfert operator

Emna Abassi   ; Lotfi Khériji

Ural mathematical journal, Tome 10 (2024) no. 1, pp. 4-17

Résumé

Here we consider a certain transfert operator $\mathrm{M}_{(c,\omega)}=I_{\mathcal{P}}-c \, \tau_{\omega},$ $\omega\neq0,$ ${c \in \mathbb{R}-\{0,1\},}$ and we prove the following statement: up to an affine transformation, the only orthogonal sequence that remains orthogonal after application of this transfert operator is the Meixner polynomials of the first kind.

Détail

Keywords: Regular form, Meixner polynomials, Divided-difference operator, Transfert operator, Hahn property.
Mots-clés : Orthogonal polynomials

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