The Nevanlinna-Pick problem on the closed unit disk: Minimal norm rational solutions of low degree

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Bolotnikov, Vladimir¹  Cameron, Stephen P.¹ 

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

关键词: Pick matrix;    Minimal norm solution;    Low-degree rational solution;   

DOI  :  10.1016/j.cam.2012.02.009

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free