A CHARACTERIZATION OF MEIXNER ORTHOGONAL POLYNOMIALS VIA A CERTAIN TRANSFERT OPERATOR - Emna Abassi; Lotfi Khériji (Ural Mathematical Journal, 2024)
Here we consider a certain transfert operator \(M_{(c,ω)}=I_{\mathcal{P}}-c \, τ_{ω},\) \(ω≠0,\) \({c \in \mathbb{R}-\{0,1\},}\) 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.