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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniform rational approximation
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by Li Ming Yang PDF
Proc. Amer. Math. Soc. 123 (1995), 201-206 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 201-206
  • MSC: Primary 30H05; Secondary 30E10, 41A20, 46J10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242112-7
  • MathSciNet review: 1242112