Analytic discs and uniform algebras generated by real-analytic functions

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. Dedicated to John Wermer on the occasion of his 90th birthday2000 Mathematics Subject Classification.