Abstract
The main theorem proved in this paper is as follows. There exist odd functionsf ɛC[−1,1] with the following property. LetP n be the polynomial of best uniform approximation tof of degree≦n. Then for infinitely manyn,P n has zero of orders(n)≧c logn atx=0.
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References
G. G. Lorentz,Approximation by incomplete polynomials, problems and results, in Proceedings of Conference on Rational Approximation, Tampa, Florida, December 1976, Academic Press, to appear.
T. J. Rivlin,The Chebyshev Polynomials, John Wiley and Sons, New York, 1974.
E. B. Saff and R. S. Varga,The sharpness of Lorentz’s theorem on incomplete polynomials, preprint.
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This research has been supported by Grant MPS 75-09833 of the National Science Foundation.
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Lorentz, G.G. Incomplete polynomials of best approximation. Israel J. Math. 29, 132–140 (1978). https://doi.org/10.1007/BF02762003
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DOI: https://doi.org/10.1007/BF02762003