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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniform algebras generated by holomorphic and pluriharmonic functions


Author: Alexander J. Izzo
Journal: Trans. Amer. Math. Soc. 339 (1993), 835-847
MSC: Primary 46J15; Secondary 32E25, 46E15
MathSciNet review: 1139494
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Abstract: It is shown that if $ {f_1}, \ldots ,{f_n}$ are pluriharmonic on $ {B_n}$ (the open unit ball in $ {\mathbb{C}^n})$ and $ {C^1}$ on $ {\bar B_n}$, and the $ n \times n$ matrix $ (\partial {f_j}/\partial {\bar z_k})$ is invertible at every point of $ {B_n}$, then the norm-closed algebra generated by the ball algebra $ A({\bar B_n})$ and $ {f_1}, \ldots ,{f_n}$ is equal to $ C({\bar B_n})$. Extensions of this result to more general strictly pseudoconvex domains are also presented.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1139494-6
PII: S 0002-9947(1993)1139494-6
Article copyright: © Copyright 1993 American Mathematical Society