Uniform algebras generated by holomorphic and close-to-harmonic functions.

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc $ \overline{\mathbb{D}}$ and $ h$ is a nowhere-holomorphic harmonic function on $ \mathbb{D}$ $ \partial{\mathbb{D}}$ $ \mathcal{C}(\overline{\mathbb{D}})$ an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if $ h$, where $ R$ [ABSTRACT FROM AUTHOR]