On the construction of de la Vallée Poussin means for orthogonal polynomials using convolution structures

In this paper we construct a de la Vallée Poussin approximation process for orthogonal polynomial expansions. Our construction is based on convolution structures which are established by the orthogonal polynomial system. We show that our approach leads to a natural generalization of the de la Vallee Poussin approximation process known from the trigonometric case. Finally we consider Jacobi polynomials and the generalized Chebyshev polynomials expansions as examples.