Analytic discs and uniform algebras generated by real-analytic functions

Izzo, Alexander

doi:10.1090/proc/14311

Analytic discs and uniform algebras generated by real-analytic functions
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by Alexander J. Izzo

Proc. Amer. Math. Soc. 147 (2019), 1519-1529

DOI: https://doi.org/10.1090/proc/14311

Published electronically: January 9, 2019

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Abstract:

Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic. This strengthens several earlier results concerning uniform algebras generated by real-analytic functions.

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