On the Weyl Matrix Balls Associated with the Matricial Schur Problem in the Nondegenerate and Degenerate Cases

Abstract

The main goal of the paper is to determine the Weyl matrix balls associated with an arbitrary matricial Schur problem. For the special case of a nondegenerate matricial Schur problem the corresponding matrix balls were computed in [3, part II], [7, parts III and IV], and [4, Sections 3.9 and 5.6]. The case of a degenerate Schur problem was first treated by S. N. Zinenko [22] who used essentially the description of the solution set which was constructed in [3, part IV]. Our computation of the corresponding Weyl matrix balls is based on the approach to the matricial Schur problem developed in [9]. The key instrument is here a distinguished rational matrix function θn which is associated with an arbitrarily given matricial Schur problem. This function θn contains much information on the parameters of the Weyl matrix balls. Mathematics Subject Classification (2000). Primary 47A57, 30E05; Secondary: 47A56.

The Weyl matrix balls corresponding to the matricial truncated Hamburger moment problem

“…3) Closer analysis of the blocks of the generating matrix polynomial realizing the parametrization of the solution in order to achieve information on the concrete shape of parameters of the associated Weyl matrix ball (see [9,18]) This strategy could be also used to handle the corresponding interpolation problem for J-Potapov functions. This was done in collaboration with U. Raabe and K. Sieber (see [27][28][29][30]).…”