Conformal Models and Fingerprints of Pseudo-lemniscates
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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.
KeywordsMeromorphic functions Conformal welding Conformal models Pseudo-lemniscates Fingerprints
Mathematics Subject ClassificationPrimary 30C35 Secondary 37E10
The authors thank the anonymous referees for helpful suggestions.
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