Science Fair Project Encyclopedia
Montel's theorem
In mathematics, specifically in complex analysis, Montel's theorem is an important result about families of holomorphic functions.
The theorem states that if F is a set (also called family) of holomorphic functions defined on an open and connected subset D of the complex numbers C, then F is a normal family if and only if F is a locally bounded set .
The key part of this theorem can be reformulated as follows. Any locally bounded sequence of holomorphic functions fn defined on D has a subsequence which converges uniformly on compact subsets to a holomorphic function f.
References
John B. Conway. (1978) Functions of One Complex Variable I. Springer-Verlag, New York, New York.
See also
Last updated: 05-25-2005 19:37:01
09-23-2007 01:00:40
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details