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The density of extreme points in complex polynomial approximation

Authors: András Kroó and E. B. Saff
Journal: Proc. Amer. Math. Soc. 103 (1988), 203-209
MSC: Primary 30E10; Secondary 41A10, 41A50
MathSciNet review: 938669
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Abstract: Let $ K$ be a compact set in the complex plane having connected and regular complement, and let $ f$ be any function continuous on $ K$ and analytic in the interior of $ K$. For the polynomials $ p_n^*(f)$ of respective degrees at most $ n$ of best uniform approximation to $ f$ on $ K$, we investigate the density of the sets of extreme points

$\displaystyle {A_n}(f): = \{ z \in K:\vert f(z) - p_n^*(f)(z)\vert = \vert\vert f - p_n^*(f)\vert{\vert _K}\} $

in the boundary of $ K$.

References [Enhancements On Off] (What's this?)

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Keywords: Polynomial approximation, extreme points, Chebyshev polynomials, best approximants
Article copyright: © Copyright 1988 American Mathematical Society

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