Characterization of polynomials via a raising operator (Q6540332)

\textit{B. Aloui} [Period. Math. Hung. 76, 126--132 (2018; Zbl. 1413.33013)] proved that the scaled Chebyshev polynomial sequence is the only monic orthogonal polynomial sequence which is \( U_{\xi} \)-classical, i.e., for which the application of the raising operator \(U_{\xi}=x(xD+\mathbb{I})+\xi D, \) \( \xi\neq 0 \), turns the orthogonal sequence into another orthogonal one. Here the author proves a generalization of this result for the raising operator \( \mathcal{J}_{\xi}=x(xD+\mathbb{I})+\xi_1\mathbb{I}+\xi_2 D. \)