Volume 25, pp. 121-128, 2006.

Weighted approximation of derivatives on the half-line

Katherine Balázs and Theodore Kilgore

Abstract

Weighted polynomial approximation of derivatives on the half line $[0,\mathrm{\infty })$ is considered. The weight function will be of the form $e^{-R(t)}$, a “folded” Freud weight. That is, that $R(x^2)=Q(x)$, where $e^{-Q(x)}$ is a Freud weight on $(-\mathrm{\infty },\mathrm{\infty })$. Linear processes which can be used for approximation of derivatives include interpolation, in particular using node-sets recently developed by J. Szabados.

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Key words

Freud weights, derivatives, weighted approximation

AMS subject classifications

41A10, 41A05, 65D05