Landau's Theorem

Theorem

Let $f: \C \to \C$ be a holomorphic function in the unit disk $\cmod z \le 1$.

Let $\cmod {\map {f'} 0} = 1$.

Then there exists:

a disk $D$ of radius $B$

an analytic function $\phi$ in $D$ such that $\map f {\map \phi z} = z$ for all $z$ in $D$

such that $L$ is an absolute constant where:

$L > B$

where $B$ is Bloch's constant.

Also see

• Definition:Landau's Constant
• Value of Landau's Constant

• Bloch's Theorem
• Definition:Bloch's Constant
• Value of Bloch's Constant

Source of Name

This entry was named for Edmund Georg Hermann Landau.