Publications de l'Institut Mathématique, Nouvelle SérieVol. 91(105), pp. 163–175 (2012)
|
|
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 $(r-1)$ 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.
© 2012 Mathematical Institute of the Serbian Academy of Science and Arts
|