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Analytic discs and uniform algebras generated by real-analytic functions


Author: Alexander J. Izzo
Journal: Proc. Amer. Math. Soc. 147 (2019), 1519-1529
MSC (2010): Primary 46J10, 46J15, 32E20, 30H50, 32A65
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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Additional Information

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: aizzo@bgsu.edu

DOI: https://doi.org/10.1090/proc/14311
Received by editor(s): June 25, 2018
Published electronically: January 9, 2019
Dedicated: Dedicated to John Wermer on the occasion of his 90th birthday
Communicated by: Harold P. Boas
Article copyright: © Copyright 2019 American Mathematical Society