A matrix characterization for the DνDν-semiclassical and DνDν-coherent orthogonal polynomials

We present a new structure relation for the sequence of orthogonal polynomials associated with a DνDν-semiclassical linear functional of class s  , and then we use it to obtain a matrix characterization of the DνDν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of DνDν-coherent pairs of linear functionals.