Zeros of Holomorphic Functions in the Unit Ball and Subspherical Functions
- 作者: Khabibullin B.1, Khabibullin F.1
-
隶属关系:
- Bashkir State University
- 期: 卷 40, 编号 5 (2019)
- 页面: 648-659
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204452
- DOI: https://doi.org/10.1134/S199508021905010X
- ID: 204452
如何引用文章
详细
We continue our previous results from the functions of one complex variable in the unit disk to the functions of several variables in the unit ball. Let M be a δ-subharmonic function with Riesz charge µM on the unit ball \(\mathbb{B}\) in ℂn. Let f be a nonzero holomorphic function on \(\mathbb{B}\) such that f vanishes on Z ⊂ \(\mathbb{B}\), and satisfies the inequality ∣f∣ ≤ exp M on \(\mathbb{B}\). Then restrictions on the growth of µM near the boundary of B imply certain restrictions on the distribution of Z. We give a quantitative study of this phenomenon in terms of (2n − 2)-Hausdorff measure of zero subset Z, and special non-radial test subharmonic functions constructed using ρ-subspherical functions.
作者简介
B. Khabibullin
Bashkir State University
编辑信件的主要联系方式.
Email: khabib-bulat@mail.ru
俄罗斯联邦, Bashkortostan, Ufa, 420076
F. Khabibullin
Bashkir State University
Email: khabib-bulat@mail.ru
俄罗斯联邦, Bashkortostan, Ufa, 420076