Suppose f : double-struck D sign → V is a proper holomorphic map of the unit disk double-struck D sign ⊂ ℂ onto a subset V ⊂ double-struck D sign of degree d > 0. We show that f is conjugate to either an affine map or a degree d Blaschke product. As an application we give a unified treatment of theorems of Böttcher and Schröder coordinates.
|Journal||Journal of Geometric Analysis|
|Publication status||Published - 2001|
- Blaschke products
- Proper mappings