Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after French mathematician Paul Montel. |
The theorem below says that it takes very little for a sequence of analytic functions to be normal: the functions only have to be uniformly bounded on any ... |
| Теорема Монтеля о компактном семействе функций |  |
Теорема Монтеля об условиях компактности семейства голоморфных функций или принцип компактности:
Теорема Монтеля обобщается на области D в пространстве {\mathbb C}^{n}, n>1. Википедия
Theorem 4.31 (Montel). Let D ⊆ C be a region and F ⊆ O(D). Suppose that F is locally bounded. Then, F is normal. Proof. We show that F is locally ... |
11 дек. 2022 г. · Normal implies locally bounded. By the Arzelà-Ascoli Theorem, every normal family is locally bounded. Locally bounded implies normal. |
18 февр. 2022 г. · This theorem is one of the basic results in the theory of approximation of functions of a complex variable; it was obtained by P. Montel . |
The theorem really consists of two separate parts. (1) F is equicontinuous under the assumption that F is a family of holomorphic functions that is uniformly ... |
Understanding Montel's Theorem aids in classifying singularities by showing how families of functions behave near points where they may not be analytic. |
22 мар. 2013 г. · In other words a sequence of holomorphic functions {fn} has a subsequence which converges uniformly on compact subsets to a holomorphic ... |
21 апр. 2014 г. · Montel's theorem: A family F⊂H(U) is normal if and only if it is locally bounded. (Where U⊂C, open, and H(U) is the space of holomorphic ... |
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