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

A significant extremal question is considered within the solution sets of two different nondegenerate truncated matricial Hamburger moment problems: Taking an arbitrary α∈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 α 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 α∈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.