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Proceedings of the American Mathematical Society

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A Müntz-Szász theorem for $ C(\bar D)$


Author: Tavan T. Trent
Journal: Proc. Amer. Math. Soc. 83 (1981), 296-298
MSC: Primary 46J10; Secondary 30E10
DOI: https://doi.org/10.1090/S0002-9939-1981-0624917-6
MathSciNet review: 624917
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Abstract: A Müntz-Szasz theorem is proved for the continuous functions on the closed unit disc $ \overline D $. As a corollary it is shown that if $ \gcd (n,m) = 1$, the uniformly closed algebra generated by 1, $ {z^n}$, $ {\bar z^m}$ is $ C(\overline D )$ (Minsker).


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DOI: https://doi.org/10.1090/S0002-9939-1981-0624917-6
Keywords: Müntz-Szasz theorem, Stone-Weierstrass theorem, uniform approximation in the plane
Article copyright: © Copyright 1981 American Mathematical Society