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| | In [[complex analysis]], a mathematical discipline, the '''fundamental normality test''' gives sufficient conditions to test the normality of a [[Family (disambiguation)#Mathematics|family]] of [[analytic functions]]. |
| | |
| | ==Statement of theorem== |
| | Let <math>\mathcal{F} </math> be a family of analytic functions defined on a domain <math> \Omega </math>. If there are two fixed complex numbers ''a'' and ''b'' that are omitted from the range of every ''ƒ'' ∈ <math>\mathcal{F}</math>, then <math> \mathcal{F} </math> is a [[normal family]] on <math> \Omega </math>. |
| | |
| | The proof relies on properties of the [[elliptic modular function]] and can be found here: |
| | {{cite book | author = J. L. Schiff | title = Normal Families | publisher = Springer-Verlag | year = 1993 | isbn=0-387-97967-0 }} |
| | |
| | ==See also== |
| | *[[Montel's theorem]] |
| | |
| | [[Category:Complex analysis]] |
Latest revision as of 03:06, 9 January 2014
In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions.
Statement of theorem
Let be a family of analytic functions defined on a domain . If there are two fixed complex numbers a and b that are omitted from the range of every ƒ ∈ , then is a normal family on .
The proof relies on properties of the elliptic modular function and can be found here:
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