Email this article On the Distribution of Zero Sets of Holomorphic Functions
- Authors: Khabibullin B.N.1, Rozit A.P.1
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Affiliations:
- Bashkir State University
- Issue: Vol 52, No 1 (2018)
- Pages: 21-34
- Section: Article
- URL: https://journal-vniispk.ru/0016-2663/article/view/234392
- DOI: https://doi.org/10.1007/s10688-018-0203-x
- ID: 234392
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Abstract
Let M be a subharmonic function with Riesz measure νM in a domain D in the n-dimensional complex Euclidean space ℂn, and let f be a nonzero function that is holomorphic in D, vanishes on a set Z ⊂ D, and satisfies |f| ⩽ expM on D. Then restrictions on the growth of νM 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.
About the authors
B. N. Khabibullin
Bashkir State University
Author for correspondence.
Email: khabib-bulat@mail.ru
Russian Federation, Ufa
A. P. Rozit
Bashkir State University
Email: khabib-bulat@mail.ru
Russian Federation, Ufa
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