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

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 {P-n}n >= 0 such that {JP(n)}(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. (C) 2011 Elsevier B.V. All rights reserved.