On classical orthogonal polynomials related to Hahn's operator. Issue 6 (2nd June 2020) - Álvarez-Nodarse, R.; Castillo, K.; Mbouna, D.; Petronilho, J.
ABSTRACT: Let u be a non-zero linear functional acting on the space of polynomials. Let D q, ω be a Hahn operator acting on the dual space of polynomials. Suppose that there exist polynomials φ and ψ, with deg ⁡ φ ≤ 2 and deg ⁡ ψ ≤ 1, so that the functional equation D q, ω ( φ u ) = ψ u holds, where the involved operations are defined in a distributional sense. In this note we state necessary and sufficient conditions, involving only the coefficients of φ and ψ, such that u is regular, that is, there exists a sequence of orthogonal polynomials with respect to u .