Journal Article10.1007/BF03321037
Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs
Leonhard Frerick,Jürgen Müller +1 more
2
TL;DR: For compact sets which are not 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.
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Abstract: 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
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Citations
Jackson's inequality in the complex plane and the Łojasiewicz-Siciak inequality of Green's function
TL;DR: It is proved a generalization of Jackson's inequality for compact sets in the complex plane admitting both upper and lower bounds for their Green's functions, i.e., the well known Holder Continuity Property and the less known but crucial Łojasiewicz-Siciak inequality.
6
On the Best Linear Approximation of Holomorphic Functions
Yu. A. Farkov,Yu. A. Farkov +1 more
TL;DR: In this article, a survey of Faber series partial sums for linear n-width approximation of holomorphic functions with bounded fractional derivatives in domains of tube type is presented. But it is known that the partial sums give the classical method for approximation of functions f ∈ H ∞ istg (Ω) in the metric of C(E) when E is a bounded continuum with simply connected complement and Ω is a canonical neighborhood of E.
References
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Boundary Behaviour of Conformal Maps
Ch. Pommerenke
- 27 Aug 1992
TL;DR: In this paper, the authors describe local boundary behavior in terms of curve families, curve families and capacity, and the Hausdorff measure, which is a measure of the curve families' capacity.
2.3K
Faber Polynomials and the Faber Series
TL;DR: The Faber Polynomials and the Faber Series as discussed by the authors have been used extensively in the literature for the purpose of identifying the most appropriate nouns for a given class of polynomials.
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