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Approximation on disks


Author: P. J. de Paepe
Journal: Proc. Amer. Math. Soc. 97 (1986), 299-302
MSC: Primary 30E10; Secondary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1986-0835885-0
MathSciNet review: 835885
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Abstract: It is shown that if the functions $ F$ and $ G$ are defined in a neighborhood of the origin in the complex plane and are in a certain sense like $ {z^m}$ and $ {z^{ - n}}$ with $ \gcd (m,n) = 1$, then on sufficiently small closed disks $ D$ around 0 every continuous function on $ D$ can be uniformly approximated by polynomials in $ F$ and $ G$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0835885-0
Keywords: Function algebra, Stone-Weierstrass theorem, uniform approximation in the complex plane
Article copyright: © Copyright 1986 American Mathematical Society

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