Zeros of Holomorphic Functions in the Unit Ball and Subspherical Functions
- Авторлар: Khabibullin B.1, Khabibullin F.1
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Мекемелер:
- Bashkir State University
- Шығарылым: Том 40, № 5 (2019)
- Беттер: 648-659
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204452
- DOI: https://doi.org/10.1134/S199508021905010X
- ID: 204452
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
B. Khabibullin
Bashkir State University
Хат алмасуға жауапты Автор.
Email: khabib-bulat@mail.ru
Ресей, Bashkortostan, Ufa, 420076
F. Khabibullin
Bashkir State University
Email: khabib-bulat@mail.ru
Ресей, Bashkortostan, Ufa, 420076
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