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Prescribing zeros of functions in the Nevanlinna class on weakly pseudo-convex domains in $ {\bf C}\sp 2$


Author: Mei-Chi Shaw
Journal: Trans. Amer. Math. Soc. 313 (1989), 407-418
MSC: Primary 32A25; Secondary 32A35, 32F15
DOI: https://doi.org/10.1090/S0002-9947-1989-0961629-5
MathSciNet review: 961629
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Abstract: Let $ D$ be a bounded weakly pseudo-convex domain in $ {{\mathbf{C}}^2}$ of uniform strict type. For any positive divisor $ M$ of $ D$ with finite area, there exists a holomorphic function $ f$ in the Nevanlinna class such that $ M$ is the zero set of $ f$. The proof is to study the solutions of $ \bar \partial $ with $ {L^1}(\partial D)$ boundary values.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0961629-5
Article copyright: © Copyright 1989 American Mathematical Society

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