Geodesic
Pick-Nevanlinna interpolation on finitely-connected domains
Studia Mathematica, Tome 103 (1992) no. 3, pp. 265-273
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Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let $z_0,...,z_n$ be n+1 distinct points in Ω. We show that for each (n+1)-tuple $(w_0,...,w_n)$ of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) $B(z_j) = w_j$, 0 ≤ j ≤ n. 
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     author = {Stephen D. Fisher},
     title = {Pick-Nevanlinna interpolation on finitely-connected domains},
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Stephen D. Fisher. Pick-Nevanlinna interpolation on finitely-connected domains. Studia Mathematica, Tome 103 (1992) no. 3, pp. 265-273. doi: 10.4064/sm-103-3-265-273

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