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Computational Methods and Function Theory

, Volume 16, Issue 4, pp 585–608 | Cite as

Conformal Equivalence of Analytic Functions on Compact Sets

  • Trevor RichardsEmail author
Article

Abstract

In this paper we present a geometric proof of the following fact: Let D be a Jordan domain in \(\mathbb {C}\), and let f be analytic on cl(D). Then there is an injective analytic map \(\phi :D\rightarrow \mathbb {C}\), and a polynomial p, such that \(f\equiv p\circ \phi \) on D (that is, f has a polynomial conformal model p).

Keywords

Conformal equivalence Level curves Analytic functions Conformal invariant 

Mathematics Subject Classification

30C 30A 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematics DepartmentWashington and Lee UniversityLexingtonUSA

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