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Proceedings of the American Mathematical Society

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

 

 

Nongeometric convergence of best $ L\sb p\ (p\neq 2)$ polynomial approximants


Authors: K. G. Ivanov and E. B. Saff
Journal: Proc. Amer. Math. Soc. 110 (1990), 377-382
MSC: Primary 41A10; Secondary 41A50, 41A63
MathSciNet review: 1019751
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Abstract: For an arbitrary function $ f$ analytic in the disk $ D:\left\vert z \right\vert < 1$ and continuous in $ \bar D$, we show that geometric convergence in $ D$ of best $ {L_p}(1 \leq p \leq \infty )$ polynomial approximants to $ f$ on $ C:\left\vert z \right\vert = 1$ is assured only when $ p = 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1019751-7
Keywords: Best polynomial approximation, least squares, $ {L_p}$-norm, convergence rates
Article copyright: © Copyright 1990 American Mathematical Society