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Subjects
32-XX Several complex variables and analytic spaces
32Wxx Differential operators in several variables
32W05 $\bar{\partial}$ and $\bar{\partial}$ -Neumann operators

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Zeros of bounded holomorphic functions in strictly pseudoconvex domains in $ℂ^{2}$

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let $D$ be a bounded strictly pseudoconvex domain in $ℂ^{2}$ and let $X$ be a positive divisor of $D$ with finite area. We prove that there exists a bounded holomorphic function $f$ such that $X$ is the zero set of $f$ . This result has previously been obtained by Berndtsson in the case where $D$ is the unit ball in $ℂ^{2}$ .

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Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2

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Zeros of bounded holomorphic functions in strictly pseudoconvex domains in $ℂ^{2}$