Journal of Inequalities and Applications
Volume 1 (1997), Issue 2, Pages 99-123
doi:10.1155/S1025583497000076
Weighted Lagrange and Hermite–Fejér interpolation on the real line
Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, Budapest H- 1364, Hungary
Received 14 February 1996
Copyright © 1997 J. Szabados. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For a wide class of weights, a systematic investigation of the convergence-divergence behavior of Lagrange interpolation is initiated. A system of nodes with optimal Lebesgue constant is found, and for Hermite weights an exact lower estimate of the norm of projection operators isgiven. In the same spirit, the case of Hermite–Fejér interpolation is also considered.