Premium
On a class of extremal solutions of a moment problem for rational matrix‐valued functions in the nondegenerate case I
Author(s) -
Fritzsche Bernd,
Kirstein Bernd,
Lasarow Andreas
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810054
Subject(s) - mathematics , context (archaeology) , class (philosophy) , unit disk , rational function , moment (physics) , matrix (chemical analysis) , point (geometry) , theme (computing) , pure mathematics , unit (ring theory) , rational number , algebra over a field , computer science , geometry , classical mechanics , physics , paleontology , materials science , mathematics education , artificial intelligence , composite material , biology , operating system
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)