Fundamental normality test - Alchetron, the free social encyclopedia

In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions. It is another name for the stronger version of Montel's Theorem.

Statement of theorem

Let F be a family of analytic functions defined on a domain Ω . If there are two fixed complex numbers a and b that are omitted from the range of every ƒ ∈ F , then F is a normal family on Ω .

The proof relies on properties of the elliptic modular function and can be found here: J. L. Schiff (1993). Normal Families. Springer-Verlag. ISBN 0-387-97967-0.

References

Fundamental normality test Wikipedia

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