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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Analytic discs and uniform algebras generated by real-analytic functions
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by Alexander J. Izzo PDF
Proc. Amer. Math. Soc. 147 (2019), 1519-1529 Request permission

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
  • MR Author ID: 307587
  • Email: aizzo@bgsu.edu
  • 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
  • © Copyright 2019 American Mathematical Society
  • 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
  • MathSciNet review: 3910417