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A Note on Weighted Polynomial Approximation with Varying Weights

✍ Scribed by A.B.J. Kuijlaars

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
199 KB
Volume
87
Category
Article
ISSN
0021-9045

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✦ Synopsis

It is shown that if weighted polynomials w n P n with deg P n n converge uniformly on the support of the extremal measure associated with w, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subset Z having the property that a function can be approximated if and only if it vanishes on Z.

πŸ“œ SIMILAR VOLUMES

Rational Approximation with Varying Weig
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We consider two problems concerning uniform approximation by weighted rational functions [w n r n ] n=1 , where r n = p n Γ‚q n has real coefficients, deg p n [:n] and deg q n [;n], for given :>0 and ; 0. For w(x) :=e x we show that on any interval [0, a] with a # (0, a^(:, ;)), every real-valued fun

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The class of functions that can be uniformly approximated by weighted polynomials of the form w n P with deg P F n, depends on the behavior of the extremal n n measure associated with w as introduced by Mhaskar and Saff. It is shown that if in a neighborhood of a point t the extremal measure has a d