Analytic Discs and Uniform Algebras on Real-Analytic Varieties

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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1507.05477, arXiv:1509.08041