Publications de l'Institut Mathématique, Nouvelle Série Vol. 91(105), pp. 163–175 (2012) 

ON AN INTERPOLATION PROCESS OF LAGRANGE–HERMITE TYPEGiuseppe Mastroianni, Gradimir V. Milovanovic, Incoronata NotarangeloDepartment of Mathematics and Computer Sciences, University of Basilicata, Potenza, Italy; Mathematical Institute of Serbian Academy of Sciences and Arts, Kneza Mihaila 36, Beograd, Serbia; Department of Mathematics and Computer Sciences, University of Basilicata, Potenza, ItalyAbstract: We consider a Lagrange–Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first $(r1)$ derivatives, at the points $\pm 1$. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted $L^p$spaces, $1<p<\infty$, proving a Marcinkiewicz inequality involving the derivative of the polynomial at $\pm 1$. Moreover, we give optimal estimates for the error of this process also in the weighted uniform metric. Keywords: Hermite–Lagrange interpolation, approximation by polynomials, orthogonal polynomials, Jacobi weights Classification (MSC2000): 41A05; 41A10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 May 2012. This page was last modified: 12 Jun 2012.
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