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Proceedings of the American Mathematical Society

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A necessary and sufficient condition for uniform approximation by certain rational modules


Author: J. J. Carmona Doménech
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
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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\vert\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)$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0671221-7
Keywords: Rational module, orthogonal measure
Article copyright: © Copyright 1982 American Mathematical Society