Blaschke products and proper holomorphic mappings

Christian Henriksen

Blaschke products and proper holomorphic mappings

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

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.

Original language	English
Journal	Journal of Geometric Analysis
Volume	11
Issue number	4
Pages (from-to)	624-625
ISSN	1050-6926
Publication status	Published - 2001

Keywords

Blaschke products
Proper mappings

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title = "Blaschke products and proper holomorphic mappings",

abstract = "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 B{\"o}ttcher and Schr{\"o}der coordinates.",

keywords = "Blaschke products, Proper mappings",

author = "Christian Henriksen",

year = "2001",

language = "English",

volume = "11",

pages = "624--625",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

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TY - JOUR

T1 - Blaschke products and proper holomorphic mappings

AU - Henriksen, Christian

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Blaschke products

KW - Proper mappings

M3 - Journal article

AN - SCOPUS:0141793937

VL - 11

SP - 624

EP - 625

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 4

ER -