Minimal Norm Interpolation with Non-Negative Real Part on Multiply Connected Planar Domains

In this paper we describe the unique analytic function defined on the open disc &delta :={|z|} < 1} which has least Hsup2 (&delta) norm, ||f||sup2 = 1 over 2pi 2pi 0 |f(esupi0)|sup2d0 among all functions with nonnegative real part on &delta satisfying a finite number of interpolation conditions. Various extensions and improvements of this result are given, most notably to the case of planar domains whose boundary consists of a finite number of disjoint smooth simple closed curves.