Approximation on disks

de Paepe, P. J.

doi:10.1090/S0002-9939-1986-0835885-0

Approximation on disks
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by P. J. de Paepe

Proc. Amer. Math. Soc. 97 (1986), 299-302

DOI: https://doi.org/10.1090/S0002-9939-1986-0835885-0

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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 $G$.

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