On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case I

✍ Scribed by Bernd Fritzsche; Bernd Kirstein; Andreas Lasarow

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 284 KB
• Volume: 283
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200810054

✦ Synopsis

Abstract

The main theme of this paper is the discussion of a parametrized family of solutions of a finite moment problem for rational matrix‐valued functions in the nondegenerate case. We will show that each member of this family is extremal in several directions concerning some point of the open unit disk. These investigations are inspired by the authors' paper [23], where a similar topic is studied in the context of the matricial Carathéodory problem. We will see that larger parts of the results presented there can be extended to the rational case studied here.The main theme of this paper is the discussion of a parametrized family of solutions of a finite moment problem for rational matrix‐valued functions in the nondegenerate case. We will show that each member of this family is extremal in several directions concerning some point of the open unit disk. These investigations are inspired by the authors' paper [23], where a similar topic is studied in the context of the matricial Carathéodory problem. We will see that larger parts of the results presented there can be extended to the rational case studied here (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)