A characterization of Dunkl-classical d-symmetric d-orthogonal polynomials and its applications

摘要

In this paper, we obtain a necessary and sufficient condition on a linear operator J, defined on polynomials, and a d-symmetric d-orthogonal polynomial set ~(Pn)n<0 such that J~(Pn)n<0 is also d-orthogonal. That allows us to characterize the Dunkl-classical d-symmetric d-orthogonal polynomials as the range of classical d-symmetric d-orthogonal polynomials by an operator related to the Dunkl operator. As applications, we derive many properties of the Dunkl-classical d-symmetric d-orthogonal polynomials from the classical d-symmetric d-orthogonal polynomials.