Bharali, Gautam and Gorai, Sushil (2011) Uniform algebras generated by holomorphic and close-to-harmonic functions. In: Proceedings of the American Mathematical Society, 139 (6). pp. 2183-2189.
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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 (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h 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 is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.
| Item Type: | Journal Article |
|---|---|
| Publication: | Proceedings of the American Mathematical Society |
| Publisher: | American Mathematical Society |
| Additional Information: | Copyright of this article belongs to American Mathematical Society. |
| Keywords: | Harmonic function;plurisubharmonic function;polynomially convex |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 01 Jun 2011 11:11 |
| Last Modified: | 01 Jun 2011 11:11 |
| URI: | http://eprints.iisc.ac.in/id/eprint/38039 |
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