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.

By: Stephen D. Fisher (Northwestern Univ.) and Charles A. Micchelli

Published in: RC20608 in 1996

This Research Report is not available electronically. Please request a copy from the contact listed below. IBM employees should contact ITIRC for a copy.

Questions about this service can be mailed to .