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.
On the construction of de la Vallée Poussin means for orthogonal polynomials using convolution structures
Themistoclakis W
2004
Abstract
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.File in questo prodotto:
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