Conformal models and fingerprints of pseudo-lemniscates

Trevor Richards; Malik Younsi

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arXiv · 1506.05061

Conformal models and fingerprints of pseudo-lemniscates

Trevor Richards·Malik Younsi

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Abstract

We prove that every function that is meromorphic on the closure of an analytic Jordan domain and 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.

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Trevor Richards, Malik Younsi. 2015-06-16. Conformal models and fingerprints of pseudo-lemniscates. https://arxiv.org/abs/1506.05061

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