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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A necessary and sufficient condition for uniform approximation by certain rational modules
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by J. J. Carmona Doménech
Proc. Amer. Math. Soc. 86 (1982), 487-490
DOI: https://doi.org/10.1090/S0002-9939-1982-0671221-7

Abstract:

Let $X$ be a compact subset of ${\mathbf {C}}$ with empty interior and let $g$ be a complex function of class ${C^2}$ in a neighborhood of $X$. For $Z = \left \{ {z \in X|\partial g(z)/\partial \bar z = 0} \right \}$, we prove that $R(X) + gR(X)$ is uniformly dense in $C(X)$ if and only if $R(Z) = C(Z)$.
References
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Bibliographic Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 86 (1982), 487-490
  • MSC: Primary 30E10; Secondary 46J10
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0671221-7
  • MathSciNet review: 671221