On the Distribution of Zero Sets of Holomorphic Functions. II

2018/11/04 by Khabibullin, B. N., Khabibullina, E. B.
#31B05 #32A60 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.01407

Abstract

Let D be a nonempty domain in \mathbb Cⁿ. We give a scale of necessary conditions for the distribution of the zero set of holomorphic function f on domain D⊂ \mathbb Cⁿ under a restriction on its growth |f|≤ exp M, where M\not≡ -∞ is a subharmonic function. If n=1, D≠ \mathbb C is simply connected, and M is continuous, then this conditions are sufficient.

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