Entropy functionals and their extremal values for solving the Stieltjes matrix moment problem

Abstract

Entropy functionals and their extremal values have been studied by many authors (see, for example, [1], [2], [3], [5]). But similar functionals were not considered for solution interpolation problems in the matrix Stieltjes class. In this paper, entropy functionals over solutions of the Stieltjes matrix moment problem are defined and studied for the first time. Given integers m,n ≥ 1, we let C denote the linear space of columns of complex numbers x = col (