De Branges' Theorem

The statement concerns the Taylor Coefficient s ''a_n'' of such a function, normalized as is always possible so that ''a''₀=0 and ''a''₁=1. That is, we consider a holomorphic function of the form : $f(z)=z+\sum_{n\geq 2} a_n z^n$ which is defined and injective on the open unit disk (such functions are also called schlicht functions). The theorem then states that
	With &alpha Being A Complex Number Of	"http://wwwinformationdelightinfo/encyclopedia/entry/absolute_value" class="copylinks">Absolute Value 1 Indeed, one can show that if ''f'' is a schlicht function and ''a''<sub>''n''</sub>=''n'' for some ''n''&ge2, then ''f'' is a rotated Köbe function
	Shows: It Is Holomorphic On The Unit Disc And Satisfies ''a''<sub>''n''</sub>&le''n'' For All ''n'', But It Is Not Injective Since <i>f</i>&nbsp'(-1/2)	0

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