2018•Proceedings of the American Mathematical SocietyRequires access
Analytic discs and uniform algebras generated by real-analytic functions
Alexander J. Izzo
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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.