On the Distribution of Zero Sets of Holomorphic Functions. III. Conversion Theorems

B. N. Khabibullin; F. B. Khabibullin

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arXiv · 1811.10393

On the Distribution of Zero Sets of Holomorphic Functions. III. Conversion Theorems

B. N. Khabibullin·F. B. Khabibullin

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Abstract

Let $D$ be a domain in the complex plane $\mathbb C$. It follows from first part of our work that if a non-zero holomorphic function $f$ on $D$ vanishes on a sequence ${\sf Z}\subset D$ and satisfies $|f|\leq M$ on $D$, where $M$ is a subharmonic function on $D$, then the the distribution of ${\sf Z}$ is subordinated to the Riesz measure $ν_M$ of $M$ in a certain sense. Here we show that this result is "almost reversible".

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BibTeX RIS

B. N. Khabibullin, F. B. Khabibullin. 2018-11-04. On the Distribution of Zero Sets of Holomorphic Functions. III. Conversion Theorems. https://arxiv.org/abs/1811.10393

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