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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The relationship between the zeros of best approximations and differentiability


Author: Peter B. Borwein
Journal: Proc. Amer. Math. Soc. 92 (1984), 528-532
MSC: Primary 41A50; Secondary 41A10
DOI: https://doi.org/10.1090/S0002-9939-1984-0760939-5
MathSciNet review: 760939
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Abstract: We examine the relationship between the analytic properties of continuous functions on $ [ - 1,1]$ and the location of the roots of the sequence of best polynomial approximations. We show that if the approximants have no zeros in a certain ellipse then the function being approximated must be analytic in this ellipse. We also show that the rate at which the zeros of the $ n$th approximant tend to the interval $ [ - 1,1]$ determines the global differentiability of the function under consideration.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1984-0760939-5
Article copyright: © Copyright 1984 American Mathematical Society

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