Computational Methods and Function Theory 3 (2003), No. 1, 273--284
Copyright Heldermann Verlag 2003
Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs
email@example.com, Fachbereich Mathematik, Bergische Universität GH Wuppertal, D-42097 Wuppertal, Germany.
firstname.lastname@example.org, Universität Trier, FB IV, Mathematik, D-54286 Trier, Germany.
For a compact set K which is the closure of a Jordan domain, the Faber operator provides a well-known tool for deriving results on the error of uniform polynomial approximation on K. We show that the corresponding methods also work for compact sets which are not the closure of a Jordan domain. In particular, the cases of so-called touching domains and of Jordan arcs are considered.
Keywords: Faber operator, Dini-smoothness, uniform approximation, touching domains, Jackson theorem.
MSC 2000: 30E10, 41A10.
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