Title
The Nevanlinna-Pick problem on the closed unit disk: Minimal norm rational solutions of low degree
Document Type
Article
Department/Program
Mathematics
Journal Title
Journal of Computational and Applied Mathematics
Pub Date
2012
Volume
236
Issue
13
First Page
3123
Abstract
For the Nevanlinna-Pick interpolation problem with n interpolation conditions (interior and boundary), we construct a family of rational solutions of degree at most n - 1. We also establish necessary and sufficient conditions for the existence and the uniqueness of a solution with the minimally possible H-infinity-norm and construct a family of minimal-norm rational solutions of degree at most n - 1 in the indeterminate case. Finally, we supplement a result of Ruscheweyh and Jones showing that in case the interpolation nodes and the target values are all unimodular, any rational solution of degree at most n - 1 is necessarily a finite Blaschke product. (C) 2012 Elsevier B.V. All rights reserved.
Recommended Citation
Bolotnikov, V., & Cameron, S. P. (2012). The Nevanlinna–Pick problem on the closed unit disk: Minimal norm rational solutions of low degree. Journal of Computational and Applied Mathematics, 236(13), 3123-3136.
DOI
10.1016/j.cam.2012.02.009
