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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Estimates for best approximation to rational functions


Author: S. J. Poreda
Journal: Trans. Amer. Math. Soc. 159 (1971), 129-135
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9947-1971-0291475-6
MathSciNet review: 0291475
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Abstract: Estimates for the deviation of certain rational functions and their polynomials of best uniform approximation on various sets are given. As a result, in some cases these deviation and polynomials are explicitly calculated. For example, the polynomials of best uniform approximation to the function $ (\alpha z + \beta )/(z - a)(1 - \bar az),\vert a\vert \ne 1$, on the unit circle are given.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0291475-6
Keywords: Best uniform approximation, rational function, lemniscate
Article copyright: © Copyright 1971 American Mathematical Society