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Transactions of the American Mathematical Society

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

 

 

On the convergence of best uniform deviations


Author: S. J. Poreda
Journal: Trans. Amer. Math. Soc. 179 (1973), 49-59
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9947-1973-0320332-3
MathSciNet review: 0320332
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Abstract: If a function f is continuous on a closed Jordan curve $ \Gamma $ and meromorphic inside $ \Gamma $, then the polynomials of best uniform approximation to f on $ \Gamma $ converge interior to $ \Gamma $. Furthermore, the limit function can in each case be explicitly determined in terms of the mapping function for the interior of $ \Gamma $. Applications and generalizations of this result are also given.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0320332-3
Keywords: Best uniform approximation, closed Jordan curve
Article copyright: © Copyright 1973 American Mathematical Society