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Constructive Approximation

, Volume 45, Issue 1, pp 129–141 | Cite as

Conformal Models and Fingerprints of Pseudo-lemniscates

  • Trevor Richards
  • Malik YounsiEmail author
Article

Abstract

We prove that every meromorphic function on the closure of an analytic Jordan domain that is sufficiently well-behaved on the boundary is conformally equivalent to a rational map whose degree is smallest possible. We also show that the minimality of the degree fails in general without the boundary assumptions. As an application, we generalize a theorem of Ebenfelt, Khavinson, and Shapiro by characterizing fingerprints of polynomial pseudo-lemniscates.

Keywords

Meromorphic functions Conformal welding Conformal models Pseudo-lemniscates Fingerprints 

Mathematics Subject Classification

Primary 30C35 Secondary 37E10 

Notes

Acknowledgments

The authors thank the anonymous referees for helpful suggestions.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsWashington and Lee UniversityLexingtonUSA
  2. 2.Department of MathematicsStony Brook UniversityStony BrookUSA

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