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・ Area of responsibility
・ Area of special scientific interest
・ Area Police/Private Security Liaison
・ Area postrema
・ AREA Property Partners
・ Area Q
・ Area redevelopment plan
・ Area rule
・ Area school
・ AREA Science Park
・ Area source (pollution)
・ Area studies
・ Area Study Center for Europe
・ Area Support Unit Chilliwack
・ Area theorem
Area theorem (conformal mapping)
・ Area under the curve (pharmacokinetics)
・ Area yield options contract
・ Area-7
・ Area-to-area Lee model
・ Areado
・ Areado Grande
・ Areado Group
・ Areae
・ Areal density (computer storage)
・ Areal feature
・ Areal velocity
・ Areal, Rio de Janeiro
・ Arealva
・ Areani


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Area theorem (conformal mapping) : ウィキペディア英語版
Area theorem (conformal mapping)
In the mathematical theory of conformal mappings, the area theorem
gives an inequality satisfied by
the power series coefficients of certain conformal mappings.
The theorem is called by that name, not because of its implications, but rather because the proof uses
the notion of area.
==Statement==
Suppose that f is analytic and injective in the punctured
open unit disk
\mathbb D\setminus\ and has the power series representation
:
f(z)= \frac 1z + \sum_^\infty a_n z^n,\qquad z\in \mathbb D\setminus\,

then the coefficients a_n satisfy
:
\sum_^\infty n|a_n|^2\le 1.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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