Analytic Discs and Uniform Algebras on Real-Analytic Varieties

Alexander J. Izzo

Analytic Discs and Uniform Algebras on Real-Analytic Varieties

Complex Variables 2017-10-10 v2

Authors: Alexander J. Izzo

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.

Keywords

uniform algebras real-analytic functions analytic discs holomorphic functions real-analytic varieties continuous functions

Cite

@article{arxiv.1707.01438,
  title  = {Analytic Discs and Uniform Algebras on Real-Analytic Varieties},
  author = {Alexander J. Izzo},
  journal= {arXiv preprint arXiv:1707.01438},
  year   = {2017}
}

Comments

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

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