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Derming Wang, Saleem Watson, "A characterization of the algebra of holomorphic functions on a simply connected domain", International Journal of Mathematics and Mathematical Sciences, vol. 12, Article ID 463292, 4 pages, 1989. https://doi.org/10.1155/S0161171289000086
A characterization of the algebra of holomorphic functions on a simply connected domain
Abstract
Let A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω) where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which are singly generated and have no topological divisors of zero.
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Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
