On maximum mass measures in truncated matricial Hamburger moment problems and related interpolation problems

摘要

A significant extremal question is considered within the solution sets of two different nondegenerate truncated matricial Hamburger moment problems: Taking an arbitrary a is an element of R whether there exists one and only one solution of each of those two moment problems, which has a concentrated matrix mass at the point alpha equal to the maximum mass. The main concern of this paper is to indicate that for the first moment problem (Problem (THM')(2n)), the answer is "yes"; however, for the second moment problem (Problem (THM)(m)) the existence is not generally fulfilled, and it holds if and only if alpha is an element of R has to satisfy some additional condition. These observations further serve as starting point to look for the corresponding extremal feature for three (nondegenerate) matrix interpolation problems of Nevanlinna Pick type based on the so-called block Hankel vector approach. (C) 2014 Elsevier Inc. All rights reserved.