Zeros of Holomorphic Functions in the Unit Ball and Subspherical Functions
- Autores: Khabibullin B.1, Khabibullin F.1
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Afiliações:
- Bashkir State University
- Edição: Volume 40, Nº 5 (2019)
- Páginas: 648-659
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204452
- DOI: https://doi.org/10.1134/S199508021905010X
- ID: 204452
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Resumo
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.
Sobre autores
B. Khabibullin
Bashkir State University
Autor responsável pela correspondência
Email: khabib-bulat@mail.ru
Rússia, Bashkortostan, Ufa, 420076
F. Khabibullin
Bashkir State University
Email: khabib-bulat@mail.ru
Rússia, Bashkortostan, Ufa, 420076
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