Pick-Nevanlinna interpolation on finitely-connected domains

Volume 103 / 1992

Stephen D. Fisher Studia Mathematica 103 (1992), 265-273 DOI: 10.4064/sm-103-3-265-273


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.


  • Stephen D. Fisher

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