Uniform algebras generated by holomorphic and pluriharmonic functions

Izzo, Alexander J.

doi:10.1090/S0002-9947-1993-1139494-6

Uniform algebras generated by holomorphic and pluriharmonic functions
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by Alexander J. Izzo PDF

Trans. Amer. Math. Soc. 339 (1993), 835-847 Request permission

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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