On some operators varying the dimensional parameters of d-orthogonality

In this work, we solve a characterization problem which consists to find III d -orthogonal polynornial sets (d-OPS) of Sheffer type. Then e consider its corresponding hierarchy problem That allows us to btain several couples T) where P is a d-OPS and T is an operator acting on polynomials for which TP is a dr-orthogonal polynomial set (d-OPS), d not equal d We express some of these operators as infinite order erential operators Then, we state some of their properties