Generators for $A(\Omega )$
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 by N. Sibony and J. Wermer PDF
 Trans. Amer. Math. Soc. 194 (1974), 103114 Request permission
Abstract:
We consider a bounded domain $\Omega$ in ${{\mathbf {C}}^n}$ and the Banach algebra $A(\Omega )$ of all continuous functions on $\bar \Omega$ which are analytic in $\Omega$. Fix ${f_1}, \ldots ,{f_k}$ in $A(\Omega )$. We say they are a set of generators if $A(\Omega )$ is the smallest closed subalgebra containing the ${f_i}$. We restrict attention to the case when $\Omega$ is strictly pseudoconvex and smoothly bounded and the ${f_i}$ are smooth on $\bar \Omega$. In this case, Theorem 1 below gives conditions assuring that a given set ${f_i}$ is a set of generators.References

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Additional Information
 © Copyright 1974 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 194 (1974), 103114
 MSC: Primary 32E25; Secondary 46J15
 DOI: https://doi.org/10.1090/S00029947197404198389
 MathSciNet review: 0419838