Montel's theorem
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In complex analysis, an area of mathematics, Montel's theorem, named after Paul Montel, is an important theorem about sets (also called families) of holomorphic functions.
[edit] Montel's theorem
Given a family F of holomorphic functions defined on an open subset D of the complex numbers C, then F is a normal family if and only if F is locally bounded.
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 compactly to a holomorphic function f.
[edit] References
- John B. Conway (1978). Functions of One Complex Variable I. Springer-Verlag. ISBN 0-387-90328-3.
- J. L. Schiff (1993). Normal Families. Springer-Verlag. ISBN 0-387-97967-0.
[edit] See also
This article incorporates material from Montel's theorem on PlanetMath, which is licensed under the GFDL.
