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Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 21–34 | Cite as

On the Distribution of Zero Sets of Holomorphic Functions

  • B. N. Khabibullin
  • A. P. Rozit
Article
  • 27 Downloads

Abstract

Let M be a subharmonic function with Riesz measure ν M in a domain D in the n-dimensional complex Euclidean space ℂ n , and let f be a nonzero function that is holomorphic in D, vanishes on a set ZD, and satisfies |f| ⩽ expM on D. Then restrictions on the growth of ν M near the boundary of D imply certain restrictions on the dimensions or the area/volume of Z. We give a quantitative study of this phenomenon in the subharmonic framework.

Key words

holomorphic function zero set subharmonic function Riesz measure Jensen measure 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bashkir State UniversityUfaRussia

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