Behavior of polynomials of best uniform approximation

Authors:
E. B. Saff and V. Totik

Journal:
Trans. Amer. Math. Soc. **316** (1989), 567-593

MSC:
Primary 30E10; Secondary 41A25

DOI:
https://doi.org/10.1090/S0002-9947-1989-0961628-3

MathSciNet review:
961628

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Abstract: We investigate the asymptotic behavior of the polynomials of best uniform approximation to a function that is continuous on a compact set of the complex plane and analytic in the interior of , where has connected complement. For example, we show that for "most" functions , the error does not decrease faster at interior points of than on itself. We also describe the possible limit functions for the normalized error , where , and the possible limit distributions of the extreme points for the error. In contrast to these results, we show that "near best" polynomial approximants to on exist that converge more rapidly at the interior points of .

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0961628-3

Article copyright:
© Copyright 1989
American Mathematical Society