On normal families in Cn
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DOVBUSH, Peter. On normal families in Cn. In: Complex Variables and Elliptic Equations, 2022, nr. 1(67), pp. 1-8. ISSN 1747-6933. DOI: https://doi.org/10.1080/17476933.2020.1797703
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Complex Variables and Elliptic Equations
Numărul 1(67) / 2022 / ISSN 1747-6933 /ISSNe 1747-6941

On normal families in Cn

DOI:https://doi.org/10.1080/17476933.2020.1797703

Pag. 1-8

Dovbush Peter
 
Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
 
Disponibil în IBN: 30 iunie 2022


Rezumat

We show that a family (Formula presented.) of functions holomorphic in a domain (Formula presented.) is normal if all eigenvalues of the complex Hessian matrix of (Formula presented.) are uniformly bounded away from zero on compact subsets of Ω.

Cuvinte-cheie
32A19, Holomorphic functions of several complex variables, Normal families, Zalcman's lemma