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Proceedings of the American Mathematical Society

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

 

 

Uniform rational approximation


Author: Li Ming Yang
Journal: Proc. Amer. Math. Soc. 123 (1995), 201-206
MSC: Primary 30H05; Secondary 30E10, 41A20, 46J10
MathSciNet review: 1242112
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Abstract: Let K be a compact subset of the complex plane $ \mathbb{C}$, and let $ P(K)$ and $ R(K)$ be the closures in $ C(K)$ of polynomials and rational functions with poles off K, respectively. Suppose that $ R(K) \ne C(K),\lambda $ is a nonpeak point for $ R(K)$, and g is continuous on $ \mathbb{C}$ and $ {C^1}$ in a neighborhood of $ \lambda $. Then $ P(K)g + R(K)$ is not dense in $ C(K)$. In fact, our proof shows that there are a lot of smooth functions which are not in the closure of $ P(K)g + R(K)$.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1242112-7
Article copyright: © Copyright 1995 American Mathematical Society